Can anyone shed any light (sorry!) on this

My '53reg Dti elegance has been parked up since last Nov, & when I tried to start it last weekend it didn't want to know, low battery, freezing cold, etc, Eventually I got it started after a brief charge & a jump from my other Vectra.

But now the interior light(s) dont work on opening the doors, any of them, but they work with the switch on the light.

The light is the three button type, so they cannot be disabled at the light, also the light doesn't come on when I remove the ignition key from the lock as it normally does, or when unlock the car with the remote control

Any ideas, boys & girls?