Therefore, the remote is functioning, but not talking to the box. If the box is receiving, as it seems to be by your test with the other remote, you probably just need to reset the remote. Either on the Sky help pages or just Googling throws up many suggestions for solutions.
Once you get the Sky remote talking to the box, you'll then need to find the code to get it to talk to your tv. There is a guide for how to do this on the Sky site.
Also, so you don't miss your programmes in the meantime, use the buttons on the Sky box to press 'record'.