Is your's gas? If i've has a power trip out the boiler needs re-setting so it knows its safe to spark the gas.
It is a combi too isn't it?
I had a problem over a year go where the boiler would come on to heat the water, (central heating was ok) the water would get warm and then go cold and would keep doing that.
Turned out the heat exchanger between the CH and Domestic water was full of gunk from the radiators, it needed replacing and we had to strip the rads off the walls and wash them out fill up with a system cleaner and water, then we had to drain it again 3 weeks later and re-fill with inhibitor and water.
All ok so far apart from a bit of air locked in the sysyem somewhere.
No offence Custom but what you have said is a big can of worms.
check water pressure. this can stop the boiler starting up.