Sounds like a starter/solenoid problem. I group the two together as the repair for either is probably a rebuilt starter.
The proper test is to view the activation circuit for battery volatge and then to verify the lack of voltage drops on the positive and negative sides of the circuit.
The activation wire energizes a electromagnet that pulls the drive gear into the ring gear as the switch is simultaneously closed to the starter. At that point the positive side should have within .1 to .2v of battery voltage and the ground side (the case) should have .1 - .2v difference at most from zero volts.
Bad circuits on either side can interupt the motor as it uses a lot of current.
Bosch Master, ASE Master, L1
33 years MB technician