There ARE other experts here more qualified on specifically GM cars because that's what they mainly work on. My specialties are brakes, suspension and alignment, and mostly, electrical. That's why I answered your post.
There's no need to go hunting for a blown fuse yet because the brake lights are working. The issue now is there can be up to three different parts to the brake light switch. Usually they all run on the same fuse, but that isn't true on every car model. To complicate things even further, there is going to be a computer involved in the starter system whenever there's a push button starter. There could be a problem with one part of the brake light switch that's not related to the brakes lights, or there could be a problem with that computer.
If by some chance you were using the cruise control the last time you drove the vehicle, and it stopped working during that trip, that would suggest a fuse for that circuit had blown. I suspect though that's a clue we don't have.
Next, even if you were lucky enough to find a blown fuse, it blew for a reason. I have some tricks for locating the cause of that, but if checking the fuses is difficult for you, you're not going to want to tear the dash apart to diagnose an electrical problem.
You said you got towed home. Does that mean with a tow truck and the wheels were off the ground, or someone pulled you with a chain? If they pulled you, that implies you were able to get the gear shift out of "park". Most commonly stepping on the brake pedal to release the gear shift uses a solenoid that is powered by the same brake light switch circuit that tells the computer when it's okay to start the engine. That would be a clue that the computer is not interpreting the signal from the brake light switch, and we have to suspect a defective computer. If that is wrong, and you still can't get the gear shift out of "park", that points to a less-serious cause, ... Not a computer problem.
Unfortunately, with all the computers the engineers have hung onto every part of our cars, you need a scanner to view live data and to command the computers to do things. You might consider asking at a few local auto parts stores that rent or borrow tools if they have a scanner to loan out. Every brand and model is different, but together we should be able to figure it out. Basically you want to look at the computer involved with the starter system. That is usually the Engine Computer or the Body Computer / radio. The brake light switch will be listed as something like "pressed" or "released", or "yes" or "no". Regardless of how it's listed, you should see it change when you press the brake pedal.
By the way, be sure you checked all of the brake lights, meaning the center high-mount light AND the two in the corners. The center light is fed right from the brake light switch on its own circuit. The other two can be on the same circuit or a separate one, possibly with their own fuse. It depends on whether the brake lights and the rear turn signals are the same bulbs. A lot of vehicles have gone to separate bulbs to remove the turn signal switch as part of the brake light circuit. (That makes it miserable to wire a trailer connector). Also, any rear signals that are yellow are separate from the brake lights.
I realize that may be hard to tell unless you can watch them when a helper turns things on and off, but that is one of the clues or observations we look for. Also, if you can get the chimes to pipe down for a few seconds, listen if you can hear the click of the solenoid near the gear shift lever when you press on the brake pedal. If you hear a light click, that part of the brake light switch is working, (and you should be able to shift out of "park").
Thanks to a recent major house fire, I don't have access to my service manuals to see how the circuit is wired on your vehicle. Without knowing those details, my suspicion is the brake light switch is defective. The section that controls the brake lights is okay, but a different part of it controls the cruise control, and possibly the shifter lock and starter system. To add more confusion, which isn't my intent, failing switches typically work sporadically at first before they fail completely. You tried pressing the brake pedal multiple times, so at some point it should have worked. That would argue against my suspicion of a defective switch. That's where the scanner is needed, so we can see what the computers are seeing.
Sorry I have to run until tomorrow. The library is closing. Before I forget, you don't have to go to the dealer with this problem. Every good-size city has one or two independent shops that specialize in electrical problems. You might want to drop in at a couple of them. If this is a common problem that they've seen before, they might suggest what the most likely repair involves.
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Tuesday, April 15th, 2014 AT 6:19 PM