What are the symptoms of a faulty boiler stat ?

My boiler seems to be running for very short periods and the central heating hot water is not getting to the furthest rads. I have recently changed the pump due to a failure, but am concerned that the new Wilo is not powerful enough. Could this be the answer to my problems ? I have flushed out the lowest rads on the system and have tried to rebalance the system to force the water to these rads which almost worked once, but no more. My boiler definitely needs a service, but all the external controls seem to be working ok:- programmer feeding the room stat providing feed to motorised valve, which in turn operates the microswitch and provides power to the boiler and pump. So to me it seems to be a circulating problem as the water is hot at the pump in the airing cupboard. The cold rads are approx 5.5m below the pump ! which I now realise is a 5m head pump, s.it, is this what the problem is ???