We had a similar issue when we bought this house. It came with two openers, only one worked. We tried and tried to re-program the second one, no luck. Looked online for codes, nothing worked.
We bought one of those "universal remotes". What a joke.
Here is what you do.
Look on the opener itself, take down the model number, manufacturer, and serial number (they are all on the opener, usually on the back) and call the company. They will send you one for your opener. It's about $50, but it is the only thing that works.