I purchased a Sempron 3100+ from Newegg.com on 1/23/2006. It has since stopped working (verified by testing all components separately... it's definately the proc). But when I try to register it on AMD website, to be able to RMA it, it says the serial number doesn't exist in the database. I double checked that I entered it correctly, but it just won't take it. Also, when I tried to enter the purchase date, it just turned red and wouldn't let me continue on to the serial number spot. But as soon as I deleted the date from the form, it let me go on.
Considering you bought it from Newegg, I'm going to assume you are in the US. Given that, see here. The phone number for warranty service is on that page, and it is generally recommended that you use that for RMAs.
Finally got around to calling them. The guy I talked to registered my CPU, but now I have to log into the warranty services website and finish the RMA from there. Unfortunately, I don't know what my password is for that website! Why I try to use the "Forgot your password..." link, it just takes me to a blank page. I'm not overly impressed with AMD's support site!