I would check that the door switches work properly. Each door has a switch which detects when the door is fully shut. When the door is fully shut the interior lights should start to dim off.
It's possible that you may have multiple problems but I would start with the door switches first.
1998 Mercedes E320, 200K Miles
2001 Acura 3.2TL, 178K Miles
1992 Chevy Astro, 205K Miles