It can be the starter motor.
My story short:
- The started motor died on me after 5 hours. Just barely made the engine turn with compressions, but could turn the engine without plug just like your's does.
- Changed all the cables (warranty), no help
- Renewed two batteries (one in warranty from GG with greater CCA), no help
- In the mean while broke four or five kick starters due to flywheel cutting the woodruff key and rotating on the axle (thank's once more for all the help I got here)
- After all this I got a new motor and bang, everything worked, until...
- My Bendix broke down
(the gear broke free from the axle)
- Got new Bendix (warranty) and now it works great, so far
So if you have full battery and upgraded wires, and it still does not turn, ask a new motor to test.