Q: Hooked up battery backwards everything works but engine won't crank

There is a good chance another circuit may have been damaged by the reverse installation of the battery. Hire an experienced technician inspect all of the circuit protection devices for problems. All main fuses must be checked for damage, then you can go around testing all of the vehicles accessories. The starter may be experiencing a failure as well and must be checked. If everything else in the vehicle works, you may be able to tap on the starter body if you can gain access safely. A few light taps may do the trick, otherwise it may need to be replaced. I’d suggest having the car looked at by a certified mechanic, such as one from YourMechanic, who can diagnose your starting issue and make the necessary repairs to your vehicle.