No door ajar message but in the past someone tried to break into the rear hatch and it is non-functional. I will look there. Thanks.

 

If the latch didn't work, you'd get a "door ajar" or "liftgate/lift glass open" or something like that. The dome lights and puddle lights all are on the same circuit, and are controlled by the instrument cluster which contains the dimmer circuitry for slow on/off for the lights. You'll have to troubleshoot the circuit, check that the instrument cluster receives all the signals it needs for turning off the dome lights and other components involved in this.