'96 Toyota Camry Indicator Lights Won't Turn Off Even With Key Out of Ignition. Help Please.

My '96 Camry started fine yesterday and drove it to the bank. When I
turned the car off, I noticed all of the indicator lights stayed on even when I
took the key out of the ignition. I happened to press the brake and all the
lights shut on and off as I pressed and released the brake. Very weird. I
tried to start the car again and it was hard to turn over, but it did start. I
turned the car off again and all the indicator lights shut off as normal and
restarting was not a problem at all. I then went to another store and the
same thing happened. I pressed the brake and the indicators turned off.
When I finished shopping, I started the car with no issues, but when I when
to engage into reverse, the safety lock on the shifter wouldn't let me go into
gear. I pressed the brake, still nothing. I also noticed my brake lights would
not turn on when the brake was pressed. They were working just 2 hours
before. Needless to say, I was stuck in the parking lot which is a whole
other story. What can be happening here, because I don't think it's the
brakes themselves. I think something is creating havoc in the system, but I
don't know what. Any ideas? Suggestions? Tom