Have it on a stand/boat transom? Tilt pin needs to be in place (the rod and clip that you use to adjust the trim). When you lower the tilt and reverse lock lever (plastic handle -- sounds like you found that OK), a spring controlled locking lever clamps to the tilt pin to keep the motor from swinging up when in reverse. Raising the handle should release the lock so you can tilt the motor.
Springs and the rest of the mechanism under the stern brackets corrode or rust, and that can be a problem, particularly in salt water. In addition, there is a shallow water drive bracket under there that sometimes hangs up. Try oiling up the mechanisms, and check for corrosion, damage, etc.
