New openers are cheap, quieter, and won't waste hours of your time trying to troubleshoot. Unless you just want to tear into it for fun, I wouldn't consider trying to fix it.

What you need to do is figure out what caused it to fail in the first place. These things do wear out with time, and if it's been a long time perhaps there's no issue, but usually there's a cause.

When was the last time the spring was replaced? They wear out with time, putting the door out of balance and making more work for the motor. Tightening the spring (a very dangerous operation if you don't know what you're doing) is not a real fix. It can lessen the most severe strain on the motor, but it will not balance the door. It will just cause too much return force when the door is raised. Also check that the tracks are straight and parallel, clean and lubricated.

Basically, you don't want to put a new motor on only to have it break in a year or two. Make sure the door is in good shape. You should be able to disconnect the motor / drive chain and move the door with your arms. If it's very hard to open or close, that's a problem that needs to be addressed.