Although my hot water works, why won't my radiator come on?
The most obvious thing that springs to mind is that you have air in your system.

Do the pipes between the radiators get hot, or the bottoms of the radiators but not the top?

If so then you need to bleed your radiators. You should have a little key with a square hole. Carefully open the valve at the top of the radiator a very small amount - you should hear a hissing sound of air escaping. Wait until water starts to dribble out - use a cloth to catch this. Repeat for all radiators.

For more information, pictures and a couple of videos see The Ultimate Handyman

UPDATE

Turn your thermostat all the way up - to make sure that it registers the current temperature as too cold - then the boiler should kick in. If not then it's the thermostat. If the boiler does kick in check the central heating return pipe - this should get hot after a few minutes. If not then there's either an airlock in the pipes themselves or the pump isn't working.

Can you hear the pump turning. If not there's a screw head in the centre of the pump which controls the speed of the pump (see the pictures here). Turn this clockwise. If the pump still doesn't turn you may need to replace it.

It could also be the electronics in the boiler not sending the signal out to the pump.

At this point consulting a heating engineer would be your best option.