What are you trying to do with your computer? Honestly it is most likely time to upgrade. I myself like to use old tech but even I had to admit my single core cpu was not useful anymore.
If you just want to upgrade the graphics card for playing old games then you need to check to see if your computer has an open PCI-E slot. That sounds old enough that it may even be an AGP slot.
Also is the case a full size one or a compact form factor one?