Transmission won't go into overdrive

Hello, This could just be a bad solenoid, transmission position sensor, or a number of other, more serious issues. Diagnosing the vibration should begin by identifying where it is felt, and if it is felt in the steering wheel, try balancing the tires first. The best thing you can do when buying any used car is having a pre-purchase inspection completed by a certified technician. That will flush out most if not every problem the vehicle has.