The only way to check the roomstat, is to turn the power off remove the front of the stat, could be upto 4 wires, earth, live, neutral & switched live to the boiler/pump. turn on electric with a neon screwdriver there should be power to live, with clock turned on. if the stat is turned down there should be no power to switched live, turn the stat up & there should be power to sw live. if there is power to the sw live all the time, the stat is faulty.
If the r/stat is ok, then does the system have a 3 way valve or zone valves?
If not sure, is there a cylinder stat on the side of the cylinder?
If there isn't, I'm guessing your boiler is at the bottom of the house, therefore your problem lies with a faulty anti-gravity valve, plumber req'd.
If there is a cylinder stat you might have a 3 way valve might be in your cylinder cupboard, 3 pipes into it, looks like a T with a box on it. 1 pipe goes into the cylinder, the pipe at the opposite side is the heating supply, now if this has a gate valve on the heating side, turn it off. If this stops the radiators getting hot, you need a new 3 way valve.
If it's zone valves there will be 2 valves, identify the heating valve, if it has a gate valve next to it, turn it off, if rads stop getting hot, new 2 port zone valve req'd.
Hope this helps.All in all you probably need a plumber