2002 Mazda Protege - light front damage

2002 Mazda Protégé, milage 42000, I rear ended another car at a slow speed (less than 15 mph) due to extremely slick road. Their car did not show any damage at all, mine has a cracked front bumper and crooked front grill, radiator untouched, airbag did not go off, headlights untouched, engine hood in perfect shape, no fluid spill. My car was running after the impact then I turned the engine off and removed the key. Ten minutes later I wanted to start the engine again and it does not crank at all although the dashboard lights up as usual. Is this the starter that gave up? To make sure that nothing got disconnected by the impact, which cables/connectors should I check myself and where are they?

Bigger problem yet is that the gear selector moves almost without any resistance through the gears and the car can be pushed forward and backwards even when in gear (D, 1, 2) or in “P” position. Is the transmission busted? How expensive would the repair be in this case. I will greatly appreciate any help/suggestions, thanks a lot!

Michael