Is it possible to replace just the garage door opener console?
Many garage openers and remotes use a standard radio code for communicating, with the ID number programmed by a bank of DIP switches; you just have to set the remote's DIP switches to match the opener's. It sounds like your door, though, works with remotes that each transmits a unique ID, and your opener's controller can be taught that ID.

There are, however, "universal" remotes. For example, Liftmaster sells remotes that work with a broad variety of openers; if you check their compatibility table you may find one that works for yours. If you still have one working remote then you're probably in luck; a new remote can "learn" from the old one.