no restart

2005 Aveo 1.6 automatic trans. Plastic idler pulley grenade threw timing belt bent all valves but pistons are ok.
Replaced water pump, new head . Got it to start but idled high for awhile then idled down. Once I turn engine off it wont restart unless it sits any where from 2 to 24 hrs. car sat for a couple years got it started today but same thing, idled high then idled down, I jacked up front of car to put it in gear and let it run through its shift points to let pcm relearn but it wont shift. Plus I cant get key out of ign unless I disconnect the pos cable off battery. Is the pcm bad?
Can it be tested? Will a bad pcm cause the no restart and not shifting through gears? I have no clue what to do next.

So there is nothing from the tranny at all, or does it engage when shifted? On the no-restart, have you tried to diagnose spark or fuel by spraying some carb cleaner/starter fluid into the intake? A realtime data scanner (Torque, etc) would likely be a big help to getting through these issues.

Tell us a bit more about how it developed?

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Fairfax Towing