If you don't mind not having it for 2 weeks, it's not that bad.
My repair experiences with Sony UK were surprisingly painless, given Sony's reputation for crap after-sales support. (I still think that's true, but excluding the repair division, who rock
Doesn't matter if you haven't registered it - Neither had I, but when I rang up they registered me over the phone (Just need name, addy, TH55 serial no. etc. The usual basically.)
The guy literally asked me when I bought it, didn't ask for confirmation or anything, so you should be okay
I think my serial number was definitely inside the warranty date 'tho so then he didn't need to check, but if you have one that is outside the warranty date they might ask for confirmation of purchase.
After that, the sent a DHL guy round (Nice guy, but he had a cold, which I caught! Gah!) with a itty bitty box - You open the box, take out the DHL bag, put your (Backed up) TH55 into the itty bitty box (REMEBER TO REMOVE the Stylus, Lanyard, Case and MemoryStick first!! Might wanna leave the screen protector just in case - Had some reports of screens coming back scratched...).
Put itty bitty box in DHL bag and give it back to the DHL guy.
Then wait for 2 weeks, trying to pretend your GameBoy is a PDA to curb the withdrawl symptoms, and then voila! Your TH55 comes back fixed
In theory anyway... as with all things YMMV!