(I'm not an expert, but I play one on the internet...)

Most cars have a switch on the brake pedal arm that controls the brake lights, it also is what allows the shift lock solenoid to engage and allow shifting out of park.
It's possible that that switch is frozen or stuck with the system thinking your not putting your foot on the brake, which would explain the lack of brake lights and the solenoid not engaging and releasing the shift lever.

I would get all contortionist, get a flashlight, and stick my head up under the drivers foot well and look for that switch and 'poke at it'.


Now fair warning, my car '90 240 wagon does not have the shift lock system for some reason. I can shift into any gear with or without the brake depressed.