I'm currently trying to play Diablo 3 on my way outdated computer, it gets me around 30-50 fps when I'm not doing anything but drops to around 10s or single digit frames when the action starts and gets worst when I'm playing with others. While rebuilding a new system would probably be my best solution, being financially responsible/cheap, I just can't justify spending $500 or so on a new system just to play one game; aside from playing Diablo 3, it runs everything else I need just fine. I was wondering if replacing my GPU would do anything for me or is my CPU just beyond hope and would bottleneck a new GPU? If replacing my GPU is a viable solution, what would be a good GPU? I plan on playing the game on all low settings btw.
Unfortunately most cards more powerful than your 8800GT will be held back by that old CPU of yours. You can get something a little bit more powerful like a Radeon HD 6770 or a GTX 550Ti. Anything beyond those two cards will likely be bottlenecked by your CPU. Another option would be to get a more powerful card, and accept that you won't see the full potential of that card until you put it in a new build at a later date.
Another thing you have to worry about is internet connection speed with Diablo III. A lot of the game's processing is done server side, even in single player mode, so if you have slow internet, a better GPU isn't going to help you too much. The fact that your performance is really dropping when playing with others does seem to indicate that internet connection speed may be where you real issue is. An 8800GT is old, but it should be able to handle the game fine on low or medium settings on your current system.