@ greymattr: The core upgrade idea is one I have used for some time and it's a handy way to keep the system fresh without having to buy a whole new box every couple of years.
If you decide on the more complete upgrade rather than just a card or card/PSU then do some reading first. Building a system is not that hard, but there are mistakes that can be made, particularly when installing a new motherboard.
It may not be possible to use the preloaded Windows or recovery disc (if present) with a new configuration in which case you'll need a new OS which will add to the cost and time needed. Either way it would be wise to back up your data, fully reformat the hard drive/s and reinstall from scratch if you do the full upgrade.
For now, I would suggest you replace the card and PSU to start with and see how things pan out. If that upgrade is enough, then that's fine, if you need the CPU/MB upgrade, well, you were going to get the PSU/card anyway, were n't you;)