kids hooked up charger backwards

Does it start and run with the key?

Here's what you could have damaged:

Fuses / fuse links and there could be several in that vehicle. Look around up at the bulkhead connector for "tagged" wires or obvious burned / melted insulation

Could have killed the alternator (diodes)

Ditto regulator

AND any other solid state "stuff" in the car, including radio / stereo

This could turn out to be an expensive life's lesson. It pays to take "an extra second."