Even though it doesn't need the power connector, it still requires a certain amount of power. Check to see what size the power supply is in that computer, you should get around a 350 seeing the card requires a 300w power supply, i have seen thoes computers come with anything from 250 - 350 soo, check... its always a good idea
anyways, the computer does have nice specs.
Chem might be able to answer this question better, but i believe that you can get a software hack for the 7600 GS to unlock the other pipelines, that will enhance your performance even more.