You may have a bad battery. It's common on Crown Vics/MGMs that when jumping a dead battery the head lights would come onand stay on even with the switch in the off position. After the battery charged for a few minutes they would go off, or you had to turn the head light switch to on and then off to reset them.
I just had this happen in my new style 2004 F-150 when the battery started going bad. When cranking, it would crank fast and slow and then the lights would come on and the electronic odometer went nuts and the gas guage went to Full.
New battery fixed it.
Also, check you battery cable ends. If they are dirty or corroded it drops the cranking juice down and makes the car think the same thing that the battery is putting out low voltage. As soon as the alternator charges up the battery, the problem corrects.
His: Blue w/Light Flint Born 02/05/03 (Wednesday)
6674 of 7838, Color sequence 102 of 327
1 of 111 Without Heated Seats
6 CD Changer in Trunk
Locking Lugs
Trunk Organizer
Real Oil Press Guage w/MM Face
Marauder Side Emblems
Rear Bumper Inserts
Nephews: Blue w/Light Flint
Born 02/05/03
6673 of 7838, 101 of 327 Blues 1 of 111 Without Heated Seats
Cars purchased 7 years apart, but are only 20 VIN numbers apart. Sequential units on the assembly line.
Hers: Black 300A w/Charcoal Born 06/25/02 (Tuesday)
2011 of 7838.
Locking Lugs
Trunk Organizer
Real Oil Press Guage w/MM Face
Factory Alarm
Marauder Side Emblems
Rear Bumper Inserts
#4 (Pound Rescue Marauder) 2003 DBP/Light Flint
120 of 328 DBP 1 of 217 with heated seats.
6705 of 7838 2003's
Built Friday 02-07-2003
Bought 09-10-2012
#5 2003 DBP/Light Flint
136 of 327 Blues 1 of 111 W/O Heated Seats
6741 of 7838 2003's
Built Tuesday 02-11-2003
Bought 05-06-14