(i) Even though only 16 months old, it would do no harm to pop in a fresh pair of batteries just to confirm that the remote control itself is still functional. With mine, a red LED lights up at the front end of the remote as well as on the Box itself.
(ii) If you're able to get some kind of picture from the Sky+ (which eliminates possibilities like dislodged SCART/HDMI connectors) then try using this 'hidden menu' which I was directed to use during a helpline call.
Press "Services" button
Press 0 on the number pad (nothing will happen yet)
Press 1 on the number pad (still nothing)
Press Select. The hidden menu appears.
Select item 7 (Sky+ Planner Rebuild)
Read the message and press Select to proceed.
You're told that the box will reboot itself when it's done but I tested it on mine just now and I had to press the Sky button to wake it up again.