1994 Corolla shift lever stuck in park and no brake lights

See if the brake lights work, if not check the fuses and brake light switch.

your gear is stuck , there is a little magic cover in front its base with tiny hole for a tiny screw driver to uncap it , and then use a small screw driver to push the lock lever down ( do that as you have your car switch ignition key on ON position ) and then you be able to shift gear to Park , then close that magic cover on that tiny hole .
if that does not work ? check if your brake lights are bad, harness melted , brake switch , or brake fuse .
Corolla tend to have that shut down of shifter as a safety feature .
if that is not the problem ?
then you have a shift solenoid kicked the bucket and need new one

are you parked on a hill you may have to rock your car

On the 1994 Toyota Corolla, there is an override switch, which is located above the gear shift under a plastic tab. ( You need something like a key or screwdriver to depress it), It will get you out of park and allow you to drive. I'm guessing however that the "brake light service switch" is the problem and needs to be fixed, so having got it moving, I would suggest you drive it to your dealer to get it examined

The most common problem brake switch, NO BRAKE LIGHTS, NO SHIFT.
the other possibilities interlock shift solenoid, that is the one that the brake switch has to activate so you can move your shifter.

First let somebody tell you is you have brake lights, if don't then replace brake switch. If you do then listen for a click inside the center console by the shifter. no click then you need the solenoid.

By the meantime remove the little square window by the shifter and stick a pen or little screw driver push the button that is inside that would allow you to shift.

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check to see if your brake lights work if they dont ,you need a brake switch ,this is a safety feature from ford it wont allow you to shift out of park

This may be caused by the failure of the Relay or Circuit that powers the Safety switch, or Failure of the Brake Light circuit Fuse/Relay, which releases the Shifter.
Look in the Power distribution and Fuse Box.
Regards,DT

thats a safety feature there is no compromise

The brake light switch is on your brake pedal.You may have more then one switch on the pedal.

If brake pedal sensor is bad, then lever cannot be taken out of Park unless you depress the shift lock near base of shift lever - pop off small rectangular tab to access.

Burned out brake light bulbs will not affect the shifting.