Craftsman 1/2 hp garage door opener; 10 years old

Background: I have been having trouble with the vacation lock turning itself on lately, causing me to be locked out of the garage. I have to enter through the front door, turn the vacation lock off, then open the garage door to pull my car in. Additionally, the lights on the motor turn themselves on periodically (and we do not have it programmed on a sensor to turn them on if someone walks through). They're even turning themselves on in the middle of the night and staying on until I turn them off in the morning.

Now, this is probably completely unrelated, but my new problem is that as of two days ago, neither my nor my husbands car remotes will open or close the garage door. We have tried reprogramming using the smart/learn button on the unit itself, tried the series of buttons that you can program with on the wall mounted remote, everything! They just aren't reprogramming. My exterior keypad isn't working either. Does anyone know what might be causing this and how I can fix it?