03 Town Car has Alpine head Unit w/changer in Trunk. Both FM and AM won't catch any Stations. CD Player works fine

car starts, runs and drives perfectly?
AC or heater blower works on high?
head lamps work fully and brightly.?
tail lamp (park) all glow? ?
brake lamps work and are bright.
check fuses?
look for connections to the radio loose or damaged

AM Radio dead means the antenna is missing wires to it bad. or missing.
FM may work say on 1 stations if the stations is like 5 miles away, all stations that are under say 25miles must work or the antenna is bad. FM, and vastly farther for AM.
we do not know where you live( a town) so can never guess
what stations are in range to you. see?

reset radio or replace

I dont remember if that year had a theft lock system or not, but I am looking into it. disconnect the negative battery cable for ten minutes and that should get you back to where you can enter the unlock code again and use the radio.

No it doesn't. The head unit is faulty and requires repair/replacement.

check all of your connections going into it may be corroded at electrical connections or the cd may need replaced

If you have volume but cannot control it, this is a common problem. The volume is optical so it may just have dust in it, but I have had zero luck cleaning them. The only solution I know is to replace the whole head unit.
If you have an HK factory stereo with no volume at all, and the four channels went out one at a time, the amp in the trunk has failed. Another common problem. The amp is on the driver side above the wheel well. You have to remove the driver side rear deck speaker to get the trunk lining off without tearing it. The screws that hold in the speaker are beneath the speaker grill in the rear deck. Good luck getting a 15-year-old speaker grill up without breaking the snaps. Slide a putty knive in from the sides to try to release them, but they will break anyway.
If the amp has failed, you can just bypass the amp but you will have no subs or tweeters. I did that while looking for a good deal on a junkyard amp. You can buy a new HK amp from BMW but they are prohibitively expensive. You could buy an alternate brand amp and add crossover circuits to power the subs and tweeters if you are really handy with electronics.

If you have an HK system in your BMW and you replace the head unit, use the antenna power wire from the new stereo as the 'on' signal for your HK amp in the trunk. Your FM may not work quite as well because the BMW head unit communicates with the antenna amplifier. Also, if you have a BMW CD changer in your trunk, no other head unit will communicate with that other than the original BMW head unit.
Other than the CD changer and the antenna amplifier, the wiring adapter that you can get from Crutchfield or from Amazon will make the stereo head unit replacement plug-and-play.
You may need a special five-sided wrench to get the old stereo out. You can buy that wrench on line if you can't force some other tool into those two cap screws that hold the stereo in.

Look in your owners manual for the fuse number and it's location.

it would be a single cd unit in the dash or a cd changer in the trunk

my lincoln town car is equipped with "alpine" premium, 6 cd changer in trunk

SOUNDS LIKE YOU HAVE A VERY EARLY MODEL CD CHANGER ALPINE UNIT THE S TYPE
USED A AUDIOVOX CD CHANGER HOPE THIS IS USEFUL