Loud clicking noise when I turn the ignition. Lights work(dim). Radio works.

Starters shot

what lights, the dial back lights, is it stock>?
the radios have 3 power sources
1 for radio and amp.
2: dial lamps (dim,) if the other cars dim-able park lamps work then
the radio lamps are bad, or not connected (1 wire)
3: memory. power.

my guess is the rad back lamps are dead.
so turn on the parking lights (Head ligths 1st click)
does dashlight up.? no, turn the dimmmer up.
do they light now? yes, and radio no?
if no radio lamp now, the lamp is bad or wired wrong or the fuse blew
that the dial feed wires to.
if not stock, any thing is possible, (infinity)

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!!!!!!!

It is probably your starter. If it doesn't make a noise when you turn it, starter. Check fuses as well.

i have NO clue

It could be But my guess is it is the safety netural switch could even be a starter you can test it but you need jumper wires with aligator clips, you can try turning on the lights and turn the key switch over and if the lights dim slightly then it means it is making contact and pulling volatage but not starting, if the lights don't dim slightly then it could be the safety netural switch. If you can work with jumper wires and a couple safety stands I can help you test it.

Sounds like starter selanoid, but first make sure battery connections are clean and tight, if sure they are then turn on headlights and try to start if still clicks and lights dim its starter.

soildoid is damaged on starter.after a few attempts to start it it may start tho

This sounds like a bad Earthing point off the ignition, fuse boards or battery, check ALL connections to the battery and earthing connections througout the vehicle, a long process, OR, you can take it to a vehicle electrician and pay them, the easiest solution is the latter.