You can report online, but it's much better to go to the store and get it replaced right away (if they have it in stock). Going online is quite impersonal and requires more steps than necessary to get the job done. We get 360's returned and replaced everyday at BB. They'll first check to see if it's a user problem and if it's not then it's swapped out. Just make sure you have all the cables, hard drive, etc that came with the 360. Also take whatever data off your existing 360 hard drive because that has to be replaced as well (if you got the one w/ the HD). If you want, you can call the store and see if they have your kind of 360 in stock.
Another thing the PRP can do is give you store credit and allow you to trade your 360 for a Wii or a PS3 (lol). Whatever works for ya.