Is there a way to transfer my iTunes songs from my Windows XP old
computer to my Windows XP new computer that I am getting without
loading up all the CDs and re-buying the songs again?

This might be helpful:

http://www.zwire.com/site/news.cfm?newsid=11965768&BRD=2035&PAG=740&dept_id=226964&rfi=6

I wonder is there is any other way to do it other than using CDs or a
hardrive. The CD way seems bad because it must take a lot of time.
Each CD only holds 74 minutes, which is not a lot, and you have to
burn it off your old computer, and then burn it onto your new one, so
it's like your doing double the work. But for now that seems ok.

After you get the new computer, take the hard drive out of it and
install it in the new one as a secondary drive on the same IDE channel
as the master drive. It'll still boot off the new hard drive but you
can copy files from the old one. In fact, launch iTunes (off the new
hard drive) and tell it to import the files from the folder on the old
hard drive. It'll copy them for you!