Is it a bosch starter ?
Could be a few things, instead bridge the terminals from the battery(input) and output to the motor, with a 50p or similar, does the motor spin, it won't engage as the solenoid has not been activated.
If it spins it may be ok, and could just be a stuck solenoid, then try a wire direct from the battery input to solenoid direct onto the wire where the ignition feed goes.
It sounds as though power is not getting through fully, plenty voltage but not enough current, sometimes the solenoid terminal builds up a high resistance, so doesn't hold the solenoid contacts(inside) firm enough to bridge the contact points inside for current to flow across into motor part.
Sometimes the laquer comes off flakes off the solenoid piston surround, the "tube" effectively surrounding the solenoid piston causing it to jam, normally worse when hot if this is the case, roll some old knackered 1000grit wet and dry paper in a roll, so the rough side is outer most, oil it and clean the inside of the solenoid to remove all the loose flaky pieces, drench afterwards with wd40 or similar, and dry out, will be perfect for another few years after that.
tabetha
tabetha