Go to click here for a pretty helpful summary of how to go about it
Try your local library for Scott Mueller's "Upgrading and repairing PCs" or go to his web site click here
My own observations are that your existing computer may have a motherboard which makes upgrading difficult. Also, you are correct in saying that putting new stuff in will produce only a marginal improvement. On that basis, why not spend a couple of months deciding how to go about building a new computer bearing in mind you will still be able to use the old jobby while this goes on.
You won't, let me stress, save much in the spondoolicks department, but, come the autumn, you could have a new, fast computer that you can show your friends and say "I built that!"
And, believe me, if it goes wrong you WILL be able to fix it, without paying megabucks for the warranty, and either staying in waiting for the engineer, or allowing 2 weeks for the thing to go back to the maker
You don't need spend a fortune either. Buy last year's top spec. Look for a motherboard bundle from Novatech or similar. Much of the assembly and testing has already been done, removing many of the "first time builder" pitfalls