All this rocking in gear is a load of crap, the only thing that will do is move the relative point of flywheel has stopped at, useful if it is trying to engage but damaged ring gear teeth, but this is not the case.
You could give the starter a knock in case solenoid is sticky, or put a lead direct from a decent battery onto starter direct then bridge and try.
Most likely dicky connection or buggered starter if boost pack didn't help.
tabetha