I'm a lazy troubleshooter. Take a screwdriver with an insulated handle and jump the external posts on the solenoid. It will bypass the internal gate. If the drive goes up, the solenoid is bad.
you can also wack the button about 20-30 times as fast as possible. that can knock corrosion off of the internal gate enough to get it to work once, or a little bit. Either can get you home if you're stuck and also verify it's the solenoid.
BTW- It's almost ALWAYS the solenoid.