I can turn my winshield wipers on but cant shut them off. I am supposed to have 3 speeds but don't even have that, and they shut off on their own. What could be the problem?

Bad pump, check fuse box under hood, look in owners manual

Well first I would check the fuse box for burned out fuses. Then I would get a simple dc power tester and see if the windshield wiper motor is getting power. If you don't have a bad fuse and the motor is still getting power I would say the motor has burned out.

The park mechanism inside the wiper motor has malfunctioned. you will need to replace the wiper motor to get the wipers to stop where they're supposed to.

check the winshield wiper fuse sometimes they have a high low wiper fuses otherwise they can be known for the winshield wiper delay switch to go out

Hmm i would first take a trip to the junk yard and replace the switch. Just in case you don't know they suppose to last few seconds before stop. Inspect the wiring, replace wiper motor if switch won't work.

Power is kept to a connector on the wiper motor so it can park itself even after you shut the switch off.
Something has gone awry with that circuitry in your wiper motor, it is 9 years old and is allowed to wear out. Get another one installed, check out youtube, could be a video showing you how to do it yourself.

I had the same thing on my Vett, it turn out to be the wiper motor, the circuit broad was bad in the wiper motor it self, replace it.

Remove wiper arms,open hood and remove plastic cowl(cover) at windshield,it is held in with plastic clips,the wiper motor is under the cover held in with 4 bolts(10mm).reinstall everything and turn on motor without wiper arms ,then turn it off so it finds its off position-reinstall wiper arms

Take it to dealer unless you can replace the wiper switch assembly yourself, a sure test is using a circuit tester. also tighten the motor housing if the nuts are loose usually GM uses 3 nuts, other wise take it to the dealer, they have the Technical Service Bulletins on your car, the non-dealers may not have them or have no clue or plain give you a false statement that they give you like a you don't have a clue, if so time to walk out and not return.

the most common problem is called the multi-function switch or turn signal switch--replace it----8 out of 10 thats the problem