definitely worth fixing I had a similar issue when I dropped my baby off to get the AC fixed and came back to find my stereo and speakers all missing. the shop paid for all of it (especially since it turned out to be an employee that did it) but I was furious. (fun fact, if you're going to steal the key, come back at night, and then lock up the truck when you're done, it kinda narrows down the suspect pool)
as to the problem at hand, I would only consider that if I knew it was the problem. you gotta track the power and see where it stops. and then do the same for the ground,. I'd hate to have you do all that work only to find out is was just a wasted ground.