The first thing to do is isolate the engine. there should be a wire (probably yellow) coming out from the engine that goes to either the G or I terminal on the ignition switch. disconnect that wire. now check for spark. if you have spark, it is a wiring issue on the mower. if still no spark, probably a coil.
transaxle - most of the time the hard shifting is due to the belt not disengaging for shipping. if there is still tension on the belt, it puts pressure on the gears and is hard or cannot shift. if it is forced, the shift fork probably will or has broken.