Maybe its just me, but I always, always keep my receipts on big purchases. My OH has had his Xbox for as long as its been out (warranty only goes for 2, I think?) and they've fixed it. The RROD isn't a warranty issue, its a fault in the system that they've acknowledged and will send you a postbox free of charge, and the turn around on it is maybe 3 or 4 days.
So unless your box died for other reasons there isn't a reason why Xbox wouldn't take a look at it? Or did you try to go through the store?
Edit:
I do know if you open the box on your own that voids anything that they would replace. So if you tried to take a look at it yourself then yes I totally get it. :)