I probably have an old problem, but I don't have the answer. I pulled hard on a stuck tape in the car cassette player to free it and it broke. I repaired the tape, but the player now plays super fast. I have cleaned it, but it still plays fast. How can I fix this?

It probably, somehow, engaged the Fast Forward gear set while it's playing. Or a potentiaometer for the DC motor got knocked way out of adjustment, or became disconnected from the circuit not being able to regulate the flow.

It's more likely that some of the broken tape is wrapped around the carriage of the pinch roller, thus jamming it and not letting it come into contact with the tape, therefore the take-up will be pulling the tape through at high (and now unregulated) speed.
Unfortunately you will probably have to remove the unit from the car to do this.
Have fun
Tony

Tony75 is on to something there. Maybe some tape got wrapped around the capstan thus causing it to run to fast because the diameter changed. Of course if it sounds like its playing in fast forwar and not just a tad fast then you got some mechanical issues with the tape deck now. never fun to fix cause the sheet metal in car tape decks is easily bent out of shape if you pulled to hard to remove the tape.
- mike

Get a new deck?
They are bound to be super cheap.