The head lights are most likely a separate issue. There is a relay that is known to have the socket overheat. I would take it one problem one at a time.

Start with the starter first. You need to check the following things closely and you most likely have done the first two already.

1. Battery Ground to Engine. That has to be a good solid connection. If in doubt, change it out.

2. Battery Plus to the starter also has to be a clean solid connection. This is normally a dragging starter or a click. But take that off the list by checking it.

3. Make sure you have the starter wire on the correct terminal. A lot of starter have a fake terminal that is very easy to mistake as where the starter wire should go. You can easily plug onto that and chase your tail if not careful. The start solenoid terminal is very close to the plus batter connection sort of hidden below it. The fake terminal is for an old ballast resistor and that has lead to several panicked posts about the car not starting after replacing a wire (as the owner of a car with crap insulation is want to do) or putting a new starter. Yes I have that merit badge for the “What have I done Post”.

4. Hung starter vs other problem. Easiest way to sort that out is by taking the key out of the circuit. Well the starter part of it anyway. If you have access to a remote starter switch, you could put that in between the battery and the starter and turn the key to pos II. Hit the switch and see if that causes the starter to engage and the car to start.

If you don't have a remote starter switch you can make a red neck one. Take a wire and crimp a spade lug on it. Pull off the starter solenoid wire and slip that wire in its place. Make the wire long enough to reach the plus battery terminal. Turn the key to pos II and slip on a leather glove and your safety glasses. Touch the wire to the plus terminal and see if the starter engages right away. If yes the voltage going to the starter is too low and you need to address that. If no it's time to replace the starter. You could also just pull it off and have it tested, that is a lot of work if nothing is wrong with the starter however.

Back to the head lights, pull back on the stalk and see if the high beams suddenly pop on. If they do, that is the classic burned up headlight relay symptom. Find the relay and pull it. If you see a burned area, there is the problem. If you pull back on the stalk and nothing happens, that points to a fuse and the big silver relay under the hood.

Hope this helps,

Paul