Irrespective of your choice of programs you should NEVER have 2 anti-virus programs running simultaneously. It's a recipe for disaster!
If you run two anti-virus programs simultaneously you might be lucky and suffer nothing worse than a slow PC. However, there's a very high risk that something extremely nasty could happen to your registry - which could be far more damaging than the effects of many of the viruses which you're trying to keep out!
To completely remove Norton, you simply need to download and run the 'Norton Removal Tool' from Symantec (who are the manufacturers of Norton):
http://service1.symantec.com/SUPPORT/tsgeninfo .nsf/docid/2005033108162039
AVG Free Edition is an excellent, free anti-virus product. As Kwicky has indicated, they've confused a lot of people recently by sending users a message that Version 7.1 is about to expire. The message comes with a large 'click here' button which takes you to information about the paid-for version. However, users who look closely at the message see that there's a much smaller link to to the download site for the new (7.5) free version. i.e. you can still get AVG completely free. It's here:
http://free.grisoft.com/
If you were using Norton's firewall (instead of, or as well as, XP's own firewall), you might need a free replacement. As PaulN90 suggests, Zone Alarm Free works perfectly alongside AVG:
http://www.zonelabs.com/store/content/company/ products/znalm/freeDownload.jsp?dc=12bms&ctry= US&lang=en
Chris