Headlights won't go off

Might these be "driving lights"?
Cars with "driving lights" have lights that are supposed to stay on all the time the engine is running.
These lights not only look like headlights, in fact some cars even have the headlights themselves come on when the engine is running. Look as some more (several) 2002 Grand Marquis's and see if they are the same.
Be blessed.

If the other head light works ,it won't be a fuse

Check every fuse in the car,won't take long &
the fuses will protect a complete circuit,not just
a couple head lights.

The light switch has a circuit breaker not a fuse.

Have you removed & tested the lamp it'self

No owners manual? Need that for fuses & bulbs/lamps

First check the fuse, the clearance lights are not factory in most cases and the wiring gets shorted from poor wiring. Once you replace the fuse see if the lights come on, if the fuse blows right away find the wiring to the clearance lights and disconnect them, if the short goes away it is a I said the wiring is shorted. If you don't have the owner's manual you should be able to download it at the link provided. It should be fuse #10 a 20 AMP in the interior fuse box. http://www.fordservicecontent.com/Ford_Content/catalog/owner_guides/97ecoog1e.pdf

Replace the switch

If you have other problems ,I have
a 1992 service manual & wiring diagrams

Turn off or time out?

Bulbs -usually burn out, all at once,haven't you had that happen

Blue Bulbs- are illegal in most states & you asked about the most
light. Won't get that from some aftermarket fancy color gimick

So Dim Lights--that is a problem obviously
You will have to have that diagnosed,I won't guess
at it. Only visual inspection & testing will establish why their dim

Sounds like a loose connection or a bad ground wire

First check the headlight relay by changing it with one of the same number in the fuse panel.If it checks out ok then you have a faulty headlight switch.

as the lights worked when you held the switch in position , check/ replace the light switch

Hello! I don't see a connection between the headlight issue and not starting...However I definitely see a connection with the accident and not starting...When you say "not starting" do you mean the starter doesn't crank the engine or it does crank the engine but won't start? Do you have a meter and a wee bit of experience using one? If you do we can isolate this fault together...Send a comment...Guru...Saailer

I’m happy to help further over the phone at https://www.6ya.com/expert/david_6df67de3b14de867

Hmm, thats verry interesting, sounds like there is a short somewhere. You should check the switch, and all the wiring. I bet it's the switch though.