I would forget about upgrading your current system, but don't assume that you need to spend gobs of money to get a great new system either, and remember that some parts of your current system may also be salvageable and may not hurt performance much at all on a new system (e.g. hard drive, optical drive).
You will almost certainly need the following new:
Case and power supply
Motherboard
CPU
RAM
Graphics card (unless onboard - with enough RAM this is not a major issue unless you want to play games)
That's really it, and you may be surprised how affordable it can be. I bought a pretty excellent system a few months ago for about $1600, including a new copy of Windows Vista x64 (which I would not recommend - transfer your old XP license over if you can and save money). My system is a 2.4Ghz Intel quad core with 8GB of RAM, a 500GB HD, Nvidia Geforce 8800GTS, and a decent motherboard, in an Antec case with a 600w power supply. If you went with a cheaper graphics card and half the RAM you could get something under $1000 these days. If that's still too much, you can easily get a still very decent machine with at least dual core at 2.4+ghz per core and 2+GB of RAM for about $500.
If you're in the US,
Newegg.com is a great place to purchase parts (provided you can build it yourself), or check out
PCClub.com for system builds (best if they have a local store in your area). Outside the US I'm not sure of the best options for a system builder, but generally an online/large chain will be cheaper and the local shops may or may not have the best knowledge and experience. Internationally Dell is becoming a better and better option as they continue to provide Windows XP and are now offering "no software bundle" options on several of their systems. Look for this option and Windows XP as I wouldn't recommend Vista yet.
Edit: Zionner, they don't even have 3.4Ghz quad core CPU's yet, at least not without overclocking.
- Oshyan