its always a matter of how much you'll be willing to spend. its possible that you could be able to pick up a Core2 for your current system, but i don't think you'll find any available (and determining compatibility could be a nightmare as well). of course, that means a new motherboard, and that opens up a whole new can of worms.
before you can really even think processor, you're going to have think about what hardware you can reuse with the new board such as the hard drive(s), disc drives, PSU, RAM, and video card (if you have one). just keep in mind that some of that hardware isn't going to transfer well or at all. if you have an AGP-based video card, then you'll have to think about a new video card as well. you'll also want to check what kind of RAM is currently installed on your system. if you have DDR, you're out of luck since all boards from the past couple of years use either DDR2 or DDR3 RAM.
you'll also have to keep in mind that it will invalidate your copy of Windows installed on your current hard drive which means that you'll have to at least uninstall Windows on that hard drive. you'll have to reinstall it and then activate it somehow depending on what version you have.
anyways, just keep these things in mind for the moment. since you'll probably have to upgrade the motherboard, you'll probably want to start thinking about just getting a new system entirely. again, though, its all going to come down to how much you're willing to spend.