My heating does not turn off?

We have gas central heating with a boiler in the kitchen, thermostat in the lounge and control box in the airing cupboard. The problem is that it either doesn't turn off despite me turning the thermostat right down so I know it is definitely on a lower setting than the current temperature and even turning it off in the control box, or, it doesn't turn on (the boiler doesn't fire up when I need the heating to come on, but its making loads of noise as if it is working).