With the battery connections reversed any LEDs wouldn't work but the only damage would be the starter would attempt to turn backwards, this is not good.
Depending on if it cranked much or at all you would also have shorted the stator and regulator.

 

The problem was the wire running from the positive post on the starter to the main circuit breaker, the first wire I checked. Replaced this wire and everything worked. I believe the solenoid clicking is due to the battery.

 

Im glad you figured it out. New battery should do the trick. Happy trails!

 

Thanks for the follow up. The wire that was fried is the only part of the circuit that is not protected by a fuse or breaker.

 

Since that wire is driving the four small circuits protected by 15 or less fuses, it's my thought the it probably had corrosion at the crimp. Could have been the originial start problem since with it bad, the soliniod of the starter would not get full voltage. When the battery was incorrect, conflicting DC current took out the high resistance. If the cable was OK, it should have taken out the 4 small fuses.

Just an opinion...

 

Try jump starting it without the existing battery, you'll see if it's the battery or not.

 

Then check the incoming voltage to see if you damaged the stator or regulator

 

Good idea, will do.