Transmission will not shift out of park

My vehicle will not shift out of park. The engine starts smoothly, but when I attempt to put it in any gear, it does not respond. I checked the shifter cable and it is still attached and moving. The transmission fluid is full but not overfilled. My right brake light is out. The right turn signal only shows on the front blinker.

I just bought the car with no history. Approximately thirty minutes before, I drove it about thirty miles. It did have a problem shifting into gear going up a hill and the rpm's got into the three's then it drove normal.