USAGE FROM MOST TO LEAST IMPORTANT: Skyrim (currently running on 'low' settings and minimum resolution), WoW, Minecraft
CURRENT GPU AND POWER SUPPLY: COOLMAX CU-500B 500W. Has only one PCI-E connector but I have 2 free SATA power connectors and converter cables and the card I want comes with molex to 6-pin converter cables.
OTHER RELEVANT SYSTEM SPECS: ABIT AB9 Pro. Intel Core2 2.4 Ghz. 2 GB RAM (tried upgrading to 4GB ages ago but the BIOS would competely halt very early in the boot). NVIDIA GeForce 7950 GT 512MB.
PREFERRED WEBSITE(S) FOR PARTS: I usually look up computer parts on newegg and then check if they're on Amazon for free shipping.
The 560ti will work on your system , you may experience some bottlenecking but I doun't think it will be too much with your resolution.
I would try upgrading the ram , you probably had a faulty stick when you tried the last time , if the timing is off on one of the sticks it will give you grief.
Get yourself a new 4gb kit, it will make a big difference with your graphics upgrade.