This sometimes happens when you park your car with the steering wheel turned too far to the right or to the left locking the steering wheel and trans. in park.
The automatic Toyota may be stuck in park because of transmission problems. The transmission may be jammed or stuck in that gear.
park safety switch on the back of the brake pedal is bad or disconnected
Did you check operation of stop lights? They are wired into same circuit--if fuse blown neither will work
There is a lever that will put it in neutral.
With just about any automatic transmission if you park on a slope and don't set the parking brake, the car rolls downhill a little bit until the transmission locks and it can't roll any farther. This can cause the car to get stuck in park. You might have to get another car to push you slightly uphill to disengage the parking pawl within the transmission (just a couple of inches, no more.) Whenever parking on a slope you should set the parking brake first, then put the car in park.
Maybe car is in park.
Park and neutral
If the car is automatic you must have the footbrake applied to shift from park.
Sounds like you have a busted linkage somewhere
You need to start the car, put your foot on the brake pedal, and then you can get outta PARK!!
You say your car is stuck in park but still shifts. I would say start with checking to see if your transmission linkage is still hooked up. That would be the first place to start.
Park for automatic transmissions, and Neutral for stick shifts.