I think if the motor is failing....it's NOT going to open when you want it to open. While it may be true that you need a new opener, I don't buy their story!
Check to see if your opener is adjusted properly. If something gets in the way of the path of the door, it may open back up, or not close at all. Also, if there is a short in one of the wires going to the button or one of the safety sensors (if you have them) something may cause the wires to touch and open the door.
If you're sure everything is adjusted properly, and nothing is in the path of the door, my guess would be that the codes for the opener are the same as some electronic device in your neighborhood.
My new opener has what they call "rolling codes", and it's more difficult to match than the standard opener. Maybe you could contact the manufacturer of the electronics and see what they say.