When we turn on the hot water taps, no water comes through at all. Our heating seems to be working fine and cold water taps are operating fine?

You give very little information. Check to see if your hot water tank has water in it. I assume your heat is radiant since you allude to it. So you know you have circulating hot water. But your radiant system is closed, the same water gets reheated so this is a non issue, it's a totally separate thing. Please re ask the question with information about how your water is heated and delivered. It could be something as simple as a stuck float or major as a leaking hot water tank. If it was just a heating element you would be getting cold water.

I like 2 Am's answer. Shows good insight. Just to be clear, are you saying that every hot water faucet is clogged and you get no water at all? We need to know everything that you know about your hot water system. Back ton you, Tom

I have run in to this problem two times and it was a different problem both times.

Once it was scale build up in the hot water tank that clogged the hot water outlet line on the hot water tank, and even clogged some of the shut-offs under the sinks.

The other time it was that the hot water outlet line on the hot water tank became blocked by a plastic heat traps. Here is an image of what they are and where they are. http://www.bradfordwhite.com/images/rotator/HeaterNipples_UNIT.jpg