If it won't bump, I'd be looking at coil or something but if it will, I had a similar problem the other week...........turned out to be the copper strap between the starter solenoid and the starter motor. It had corroded and was giving the exact symptoms you describe. I put in a new link between the motor and solenoid and its spot on again. You'll need to take the starter motor out to get to it though unfortunately.
Hope it helps!
Bigun