Combi boiler problems with hot water?

I have an Alpha Ocean combi boiler. My problem is that when I use the hot tap for any length of time my radiators get hot even when the central heating is off. Bit of a pain in the summer but we've lived with this for a while, just turning all the radiators off at the knobs except the main one in the hall that wont go off. Yesterday though, I couldn't get hot water from my taps though my water heating is always switched on. I checked the boiler and the wee light that should come on when someone turns on the hot tap didn't light up. I had to put the heating (radiators) on in order to get hot water from the taps. Can anyone identify the problems for me so I know exactly what I'm after when I hire someone in to fix it. Thanks in advance.