How does Old Gariot suggests that, when a culture does not keep the ideals of liberty, fraternity, and equality in view, and instead glorifies things like material wealth and social power, human beings suffer both individually and collectively?

Père Goriot shows that, when people value material wealth over noble values like liberty, equality, and fraternity, people suffer, because the characters in the novel suffer from the negative actions of those who place a high value on material wealth and personal status. Specifically, Père Goriot's and Eugène's family suffer consequences from those who are attempting to climb the social ladder and live a life of luxury with no work of their own.
The French ideals of liberty, equality, and fraternity exemplify the best of what France hopes to be. However, many of the characters in Père Goriot don't value these ideals. Instead, they value the things money can buy and the power of social influence. This damages society as a whole, creates a social net that thrives on dishonesty, and leads to unhappiness for individuals in that society. People don't work for the betterment of the community but rather for the betterment of themselves only.
Status in Père Goriot is obtained by having the most money or social influence. Eugène reveres his cousin because she is wealthy and has social power. It's what gives him access to the upper echelon of society, and lets him get to know Père Goriot's daughters:

He had just become aware of the fact that the Vicomtesse de Beauseant was one of the queens of fashion, that her house was thought to be the pleasantest in the Faubourg Saint-Germain. And not only so, she was, by right of her fortune, and the name she bore, one of the most conspicuous figures in that aristocratic world. Thanks to the aunt, thanks to Mme. de Marcillac’s letter of introduction, the poor student had been kindly received in that house before he knew the extent of the favor thus shown to him. It was almost like a patent of nobility to be admitted to those gilded salons; he had appeared in the most exclusive circle in Paris, and now all doors were open for him. Eugene had been dazzled at first by the brilliant assembly, and had scarcely exchanged a few words with the Vicomtesse; he had been content to single out a goddess among this throng of Parisian divinities, one of those women who are sure to attract a young man’s fancy.

He's willing to spend money that his family gives him to pursue a life like hers rather than working on his career. Père Goriot is admired by his landlady when he first moves in because he takes an expensive and luxurious room. As the years pass, and he has to move to smaller, cheaper rooms, her regard for him decreases. His daughters only appear to care for him when he's able to pay for the expensive lifestyle that they want. Without money or social influence, the characters in Père Goriot are looked down on and considered unimportant.
One way it's clear that the lack of fraternity or brotherhood is hurting the characters is evident in the interaction between Anastasie, Père Goriot's daughter, and Eugène. When Eugène mentions that he knows her father, Anastasie, her husband, and her lover all kick him out of the house:

Eugène had a second time waved a magic wand when he uttered Goriot’s name, but the effect seemed to be entirely opposite to that produced by the formula "related to Mme. de Beauseant." His position was not unlike that of some visitor permitted as a favor to inspect a private collection of curiosities, when by inadvertence he comes into collision with a glass case full of sculptured figures, and three or four heads, imperfectly secured, fall at the shock. He wished the earth would open and swallow him. Mme. de Restaud’s expression was reserved and chilly, her eyes had grown indifferent, and sedulously avoided meeting those of the unlucky student of law.

Eugène doesn't have any value to them on his own; when it's clear that he could reveal the poverty Anastasie's father lives in, they immediately eject him so that they can keep their own social status. He, himself, is also careless. He solicits money from his mother and sisters not so he can continue his legal education and support his family, but so he can live an empty life as a darling of society. Fraternity is about caring for your fellow-man; the characters in Père Goriot reject this when they choose their own selfish desire for money or status over their family. This leads to suffering on behalf of discarded individual family members, and ultimately weakens society as a whole when those connections that help create community are no longer valued.
It's clear that equality, too, has no place in the society in Père Goriot. Characters aren't equal to each other because their social position sets them apart. Eugène is only able to gain entry into the ranks of society because of his relationship with his cousin. Père Goriot works hard for his daughters but is rejected because, ironically, he cannot afford to live the life of luxury that he provides for them. If someone doesn't have the same social influence and access to material goods, they're seen as a lower person than someone who does have those things. A character like Vautrin is even willing to kill to help himself and others rise in their social position, because equality doesn't exist in the society in which they live. This is why he sets up Victorine's brother to die:

A book might have been made of her story. Her father was persuaded that he had sufficient reason for declining to acknowledge her, and allowed her a bare six hundred francs a year; he had further taken measures to disinherit his daughter, and had converted all his real estate into personalty, that he might leave it undivided to his son. Victorine’s mother had died broken-hearted in Mme. Couture’s house; and the latter, who was a near relation, had taken charge of the little orphan.

Vautrin attempts to plot Victorine's brother's death, so that he can have access to the additional money she will inherit if Eugène marries her. This is an example of how a lack of equality in society can lead to human misery. Eugène tries to stop the plot but her brother ultimately dies. Victorine's broken-hearted. To the characters in the novel, it's better to break the law and damage others in the attempt to reach a better position of social influence and material wealth. This attitude causes pain to the characters, but is also negative for the society they live in.
The characters in Père Goriot do not have liberty. They are bound to money and social influence and cannot function without them. Near the end of the novel, Père Goriot's daughters have both misused money in such a way that they're broke once again and in trouble with their husbands. Though Père Goriot provided for his daughters, they were careless and want more, leaving him bound to them both by love and honor:

For this ball she had ordered a golden gown like a setting for a jewel. Her mantuamaker, a woman without a conscience, would not give her credit, so Nasie’s waiting-woman advanced a thousand francs on account. Poor Nasie! reduced to such shifts! It cut me to the heart to think of it! But when Nasie’s maid saw how things were between her master and mistress, she was afraid of losing her money, and came to an understanding with the dressmaker, and the woman refuses to send the ball-dress until the money is paid. [. . .] She cannot. I saw that myself. Delphine will be there too in a superb toilette, and Anastasie ought not to be outshone by her younger sister. And then—she was drowned in tears, poor girl! I felt so humbled yesterday when I had not the twelve thousand francs, that I would have given the rest of my miserable life to wipe out that wrong. You see, I could have borne anything once, but latterly this want of money has broken my heart. Oh! I did not do it by halves; I titivated myself up a bit, and went out and sold my spoons and forks and buckles for six hundred francs; then I went to old Daddy Gobseck, and sold a year’s interest on my annuity for four hundred francs down. Pshaw! I can live on dry bread, as I did when I was a young man...

He is bound through obligation to their life of social status and luxury that he'll never be free. Instead, he takes away the very things he needs to survive so that his daughter can have a new dress for one night. Père Goriot dies still in bondage to this idea of a life of material goods and social influence, and his daughters don't even bother to attend the funeral. Without liberty, the man dies alone and is mourned only by the people who lived with him at the boarding house; he's never free enough to disentangle himself from his desire to give his daughters everything, and they are willing to take until there's nothing left he can give. They're damaged by the society created by the pursuit of money and status; it leaves them unable to feel and appreciate real human connection.
Ultimately, the lack of fraternity, liberty, and equality in Père Goriot keeps the characters from living meaningful, fulfilling lives and only leads to suffering, including the death of Père Goriot himself. The important things in life, like family and community, are set aside when the characters focus instead on material goods. While Père Goriot and Eugène might have lived happy, positive lives with the money and status they had, they were unable to. They, along with every other character in the novel, suffered, because the society in which they lived valued money and social position over the ideals of liberty, equality, and fraternity.