In theory, all of the cards I suggested will work on your computer. All you need is a PCI-E slot.
However, a more powerful graphics card may require a power supply upgrade as well. Your PSU must:
1) Have a PCI-E graphics power connector. This is not always needed but high end graphics card usually require one. Others can get additional power by a standard molex power connector, like the ones you connect to your drives.
2) Have a descent wattage rating. I wouldn't use any modern card with a PSU which can't provide at least 400 Watts.
3) Have at least three +12V rails which can provide at least 18 amperes each or a single rail which can provide at least 40 amperes. You can usually find this information on a sticker on the side of your PSU or its manual.
These cards I suggested are not high end though, they will probably work even if you don't have a top of the line PSU.
I can assure you that the Radeon HD 4650 will work on a descent low end PSU without problems. This card doesn't require an extra power connector, it relies on the PCI-E slot to get power, just as the 7600GT. This card is a lot faster than the 7600GT, especially the DDR3 version (get this one if you can find it).
The 8600GT requires a 350 Watt PSU and it also doesn't require an extra power connector. This card isn't the best around but it will still be around 10% faster compared to the 7600GT.
The other two will require a 400 Watt PSU but I'm not sure if they require an extra power connector or not. I can't see one at their pictures so I guess they don't but I can't confirm it. Of course these are both faster than the 4650 and 8600GT.
Anyway, try finding more information on your PSU, then we will be able to choose safely.