Radio shuts off when headlights are on

This would tell me there is a short in the wiring harness. If it was a relay it would affect only the electronics on that relay.

If the battery is fully charged, the headlights come on, etc,,,the alternator is working, as it was charging the battery the last time it was running, so I would see it as more of a starter/security issue........but becasue the radio is not coming on, I would seriously look at both the engine fusebox and interior fusebox for any issues that might be there......

Definetly sounds like an electrical problem, though

sounds like your computer is getting water seepage at the terminal connect point on the computer. take off computer connections and clean with a good electrical contact spray (buy at radio shack) . clean both the computer connecton interface and the cable plug, you may need to use a toothbrush to clean small areas. throughly dry then reconnect. try to see if you have problem again, if problem corrected then seal outside plug with silicone and this should prevent further problems.

2000 Ford Crown Victoria Car Radio Stereo Wiring Diagram
Car Radio Battery Constant 12v+ Wire: Violet/Light Blue
Car Radio Accessory Switched 12v+ Wire: Yellow/Black
Car Radio Ground Wire: Black/Light Green
Car Radio Illumination Wire: Light Blue/Red
Car Stereo Antenna Trigger: Blue
Left Front Speaker Positive Wire (+): Orange/Light Green
Left Front Speaker Negative Wire (-): Light Blue/White
Right Front Speaker Positive Wire (+): White/Light Green
Right Front Speaker Negative Wire (-): Dark Green/Orange
Left Rear Speaker Positive Wire (+): Gray/Light Blue
Left Rear Speaker Negative Wire (-): Tan/Yellow
Right Rear Speaker Positive Wire (+): Orange/Red
Right Rear Speaker Negative Wire (-): Brown/Pink

Download owner guide first printing from below link

http://www.motorcraftservice.com/vdirs/SPubs/default.asp?TYPE=OWNERGUIDE&pageid=oghome&gutsid=spubs_serv_all_new&MARKET_LANG=US-EN&YEAR=2003&VEHICLE=Expedition

after downloading go to page number 231 where you get the fuse box diagram
fuse for the radio is #7 in the fuse box diagram

it works completely

yes you can change it yourself and it is the same as an F150 and here is a website junkyarddog.com and try autozone.com or your local library for diagrams pictures and step by step instructions

check your interior fuse panel. does it look wet or corroded? is there a water leak maybe from the the window if you have a sun roof the drain could be leaking into the car. or it could just be a problem with a module or a corroded ground or other conection.

this vech was famous for the windshield leaking on the driver side lower part of windshield.. and the water drips onto the gem module and inside fuse panel and can cause may electrical problems.. a good way to tell is remove the 2 big connectors with a 10mm socket and inspect for any water in connector or where connector came from

Most likely water leak around windshield on the left side dripping down into the GEM module which is located on the back side of the interior fuse panel/