gear shifter stuck in park

I am having a problem with the gear shifter on my 1997 GMC Jimmy with automatic transmission. After driving it a week ago, I got out and tried to open the rear hatch. It wouldn't open, something that usually only happens if the car is not in park. I checked the gear shifter and it was in park, but when I would turn the key the car wouldn't start and the gearshifter button could not be depressed to shift out of park. After some messing around with the gear lever, I could get the truck started but I still couldn't shift out of park. After some more jostling around of the gear shifter I was able to get it out of park. So I drove the truck home, got into my garage, and put it in park and shut it off. The car started rolling on the minimal grade in my garage even though the shifter says it is in park. I put on the parking brake and there it has sat since last weekend. I think the gear shifter is messed up and the car is not actually in park right now. Is the gearshifter physically coupled to the transmission? Is my transmission messed up or is there a sensor on the gearshifter that tells the transmission what I want to do?

Added: I did some searching, could this be due to a bad "brake pedal switch"? Brake lights come on just fine.