can you get to the underside of the shower mixer to remove the pipes and test how much flow there is before the water enters the mixer? if ok, then the fault is with the mixer. if still poor there then you must have a blockage in those pipes after they split off from the pipes to the basin taps.
Is the pump switched by a microswitch on the tap or is it worked by a pressure switch? If it's the former you should hear the pump running. Turn on the shower and then turn on one of the taps that works and briefly stop the flow of water with your finger. If you then get a flow from the shower head it is probably a faulty switch. If there is still little or no flow then there is a pipework restriction or a faulty shower tap.
just remembered some shower heads have a turn off and on bezel on the shower head itself,look where the water comes out and see if there is a bezel you can turn.
------------- the only silly question is the one you do not ask.