Sounds liuke there is enough power getting to the car to run the normal electrics and the starter motor solenoid, but that there's not enough current getting through to actually do anything to the starter motor.
That suggests a bad/loose connection somewhere in the line that links battery +ve, to solenoid, solenoid to starter motor, starter motor to earth, earth to battery -ve.
Alternatively the starter motor may be jammed.
Can you rotoate the engine with the car out of gear?
Check the strap that earths the engine block/gearbox to the chassis is in place
Check battery connections are all tight
Check heavy cable from battery to starter motor solenoid and solenoid to motor are all tight
Check starter motor gear is disengaged properly
X, July 2015
