If you are still going to use the old computer, it might be easier to set up a LAN, especially if you want to share an internet connection, or may want to add another computer (ie a laptop or friend's computer for a LAN party). If you are getting rid of the old computer, it might be easier to just pull the hard drive out and stick it in the new computer temporarily.
Anyway, for what you asked;
How I connect two computers to exchange files? - other direct connection options, as well as ethernet
Direct Connection intro /
How to set up a direct cable connection (DCC) in Windows XP (written for parallel cables, but the procedure for ethernet should be similar)
see also;
Practically Networked howto list
Windows Networking tutorials
etc
