We had a very similar problem with ours just last week but with ours it was only the volume we could adjust with the sky remote and nothing else, no channel changes, wouldn't even go into standby. We put fresh batteries in and still nothing.
I suspected a fault within the handset so bought a new sky remote from Tesco (�14.99) which came with batteries.
I put the batteries in, aimed it at the sky box, and bingo! everything worked. Just to make sure I tried our old one again and still nothing apart from the volume control, so maybe your handset has gone too.