Try programming the thing this way. Hold the button down on the remote and then press and immediately release the smart/learn button. If this doesn't work the logic board has quit working. You might pull it out of the opener and check it for loose connections.

Don;
Thanks! That seems to have done the trick. Any ideas why it would have been opening on it's own? Perhaps a similar opener on the same frequency nearby? I am not sure if the previous owner has an opener and that was why I was attempting to re-program mine.
Again, THANK YOU SO MUCH!
Gary

Here are some things you can check.

Look at the LED light next to the SMART/LEARN button on rear of the motor unit. You may need to remove a light lens cover in order to see it. If the light is flashing rapidly this means you have a stuck button on one of your remote controls. Take the batteries out of each remote control. When you remove the batteries from the bad remote, the light will stop flashing. This remote needs to be replaced.

If one of your neighbors remote controls is inadvertently programmed into your receiver, you door will open when their remote is activated. If this happens you will need to clear out your receiver and reprogram your remote controls. Press and hold the smart/learn button for 6 seconds or until you see the small LED light near the button turn itself off. If the above steps have been followed and the symptoms continue, there may be an electronic short in either the wall control button or the receiver logic board. In this case, remove the wall control wires from terminals 1 and 2 on the motor unit. Should the symptoms persist after the wires are removed, replace the receiver logic board. If the symptoms stop with the wall control wires removed from the motor unit, replace the wall control button, and the wires leading to the wall control button.