It sounds to me like you may not have a graphics card, but rather an integrated chipset. I can understand though why would be frustrated with your distorted pets though, because I was in your shoes, until a couple weeks ago, when I got a card installed.
The thing about chipsets, is that they're not even supposed to be used for gaming. Chipsets are exactly what they sound like, they're attached to the motherboard. They use System RAM, rather than Video RAM. Chipsets are designed for schoolwork/office work. The problem with chipsets, is that if you destroy your GPU, you're also destroying your motherboard, and your CPU, and thereby totaling your computer.
Pets are a new life state, with several details: Fur, hooves, tails, long flowing, fluffy coats, and walk on all fours, as appose to standing up on two legs. This isn't a SimBot from Ambitions, or an Imaginary Friend from Generations. That is why your GPU has officially thrown in the towel.
How old is your computer? If you only have a Vista, all it takes is a new graphics card. Your best bet is to go and get it professionally installed at the computer shop. That way, you can get a warranty on your Graphics Card, and you're putting your computer in the hands of trusted people.
Another clue your GPU was in no way capable of handling pets: Check your default game options. Chances are they were put on the lowest settings with Advanced Rendering off. That's another sign your GPU couldn't handle the rendering of the Pets.
Good luck on your PC!