For more modern games I think you'd be better off starting fresh. You can build a new PC that will equal or best current Gen consoles pretty cheap.
Check this out for example:
Computer Parts, PC Components, Laptop Computers, LED LCD TV, Digital Cameras and more - Newegg.com
Thats just the base system and you'll still need a couple other things. But it will all depend on what can be re-used to save money.
For example, you could reuse the current HD, CD/DVD Drive. and case you have.
By the time you add a decent Power supply, and small GPU, I think you could swing it for around $400-500.
Then theres the question of Windows itself, if you have a legit key that can be used or if you need another copy.
For gaming, it may be cheaper to go with a console. As even last Gen consoles may give you a better gaming experience than what you currently have .. sadly.
Again, it all depends on what you need to replace, and what could potentially be reused.
of course, if money isn't a huge obstacle, you can build one beast of a machine.
I wouldn't sink much into what you currently have though as it will not yield a huge performance gain for anything beyond light gaming as already mentioned. I just think any potential upgrade budget would best be used towards a new system instead. but thats just me.