Its not the graphics card.
The best thing to do would to be to buy more RAM. This would give you a large increase in performance.
Also a large reason why its so slow could be because of Windows being old. Windows gets clogged up with registry entries over time and slows down. To remedy this you can reinstall windows or or could try a registry cleaner. Many people do not like registry cleaners though, if you are going to use one then I would suggest CCleaner.
With reinstalling you should make sure you can find drivers for the on board graphics and co. If your running XP then it they are not automatically installed and some can be VERY hard to find. Take this into account when reinstalling, maybe you have the original driver disc (if they come with them).
Hope that helps.