Re: Parking Problem
If the engine has stopped at Top Dead Centre (TDC), in theory it could take only a tiny force to flip it over TDC and the compression released could (nearly) be enough to start the engine. Although I think the momentum of the propeller would fail to complete a full compression of the next cylinder without some other force acting - perhaps from you grabbing onto the propeller having slipped on some ice or wet grass...
With the fuel and mags off, mixture at ICO and the throttle fully closed, I'm happy to man-handle light aircraft by the propeller. I am used to hand-propping though.
All in all it is pretty unlikely that the engine would start, but you really don't want it to happen, ever.
tp