Good advice in here, thanks. I'll have to open the box up a little later and see what the problem is. While moving the door up and down manually, it seemed very hard to move, so I wonder if the tracks are warped (the house is 25 years old, and this is probably the original garage door). If the gears are sheared, I'm guessing the fact that the door is hard to move caused them to shear, which probably means new gears won't last long. I'm thinking I may need to replace the door and opener.
I was a service tech for adams door in desmoines when i took time off school a few years ago..
need to know make and model of opener to accurately diagnose your problem, but it sounds like you need a new gear kit, the gears that drive the opener are normally teflon or some tough plastic and wear out after a while, especially if your door doesn't operate well, which sounds like that is the case. you can replace it on your own, but it can be tricky because you will have to reset the limits that determine how far the door goes up and down (can be frustrating if you don't know what your doing and depending on what kind of opener it is)
tracks don't typically "warp". there are a few common problems that may be the case if the door isn't working well. try putting motor oil on all the hinges and in the tracks (particularly in the radius where the door follows the bend in the track) basically any place where metal and metal rub (do not use grease, it will only make your problem worse 30 weight like you put in a car will do just fine) also oil the springs that lift the door (do not by any means attempt to adjust these otherwise if you dont know what you're doing). you could have some rollers that have worn out bearings causing them to drag. would kind of need more info to diagnose any specific problem, is it hard to pull up or down, both?
to change out the gear kit (if that's the problem) in the opener it will cost you probably $120 to have somebody come out and do it, but they will adust your door and make sure everything is working fine as well. an entire new door and opener is gonna run you close to or over $1000 to take your old one out and put the new one in depending on the size and quality.