the key light should come on everytime for a few seconds, are you sure you're not just being impatient?
Failing that, as it does eventually work i would suspect a dodgy connection or earth to the codebox.
Seatbelt wise, have you tried pulling the belt all the way out as far as it goes and check the belt for any little snags, rips etc. If it looks ok, spray a little WD40 on the belt right at the end (reel end clearly) and let it slowly wind back in and try it then, may have just got a bit twisted. If it still doesn't work i'd say just get one from the scrapyard. Not too hard to get to and in the yard you can check it works ok, and you can break stuff getting it out no bother, then when you come to your own car you should be an expert at how to get it out without breaking any trim (not that its difficult).