Battery connected backwards, now headlights don't work.Any ideas?

check fuse --power feed from battery --harness---ign switch

Alternator voltage may be to hight that make the battery to dry out,or maximum output amp not ok and battery cant be fully charge

When the battery was connected in reverse some electrical components were damaged. A motor, a relay, headlights can work both ways but not printed circuits in electronics. You are lucky you did not toast your computer!!!!!!!

If you made sure your battery connections are tight then you may need trace you hot wire for a bad connection around the fusible links that run from battery.

by replacing the battery the anti-theft code requirement has been activated
check the radio forums and comments on this site as there are ways to recover the code

If your corvette is fibreglass, then make sure there is a good earth return for everything electrical, lights, indicators, wipers, horn, etc. You can check each item individually with a dedicated negative and positive wire to the battery. This will tell you if it functions or not, ie: the water pump will buzz if working, insert tube into jar of water to see if it pumps water, if not check if the nozzle is blocked a needle my help clear it. Hope this may help.

You may have blown a fuse, check fuses first then before you try to replace the bulb again check for broken wires or the correct bulb

How about corroded battery cables (internal)

Fusible Link wiring corroded & open circuit,does
everything electrical work except the starting circuit?

Turn key & have power to starter solenoid ?
Neutral Switch !
Ignition Switch !

Tough to guess without wiring diagrams,
to see where to start testing

Can't fix what you don't know you have

This can happen when the wires to the lights come loose. If you know someone who can get in the back and check the wiring, and can hook them back up, that's probably all it is. Sometimes items in the trunk, or the back of an SUV, or just hard road bumps can shake the connections loose.

these trucks have a generic body control module in the left kickpanel. just remove the plastic trim from the drivers floor molding to access the module. inspect the wire for green dust or gel. if there is signs of this then you have a corrosion problem. disconnect you battery and then try cleaning the corrosion all off using contact cleaner and penetrating oil. once the corrosion is gone then reconnect everything and try to see if it works. If not then it is possible that the module is damaged. you will need a new one.