I had a similar problem . Water pump not working - i.e windscreen wipers working but no water being pumped through to front or back.
On my Honda Jazz 2005, there is one fuse that powers the wipers and the windscreen water motors. So I ruled out the fuse being the problem.
Removed the wheel trim cover to get to the motors, tested the connectors with a multi meter. They were fine, so whittled it down to the motors.
Decided to try tapping them with a hammer. This worked, amazingly for the rear motor but not the front motor.
Disconnected the connecting hose attached to the motor- let the water drain out fully.
Prised the motor out and then tested it by attaching it via some dodgy home made electrical wires to the car battery.
Motor did not make a noise but got warm. Though it was knackered- Re-attached it for one last try in the hope that it had been stimulated to work, and it did.
So there you go, solution - hit with hammer, if doesn't work, try some electric shock treatment.