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You either need an exorcist or a good garage door person... or both.
The occurrence of the door opening and then the remote not working could be caused by a short in either the wall switch or in the two wires leading to it. If these two wires were somehow to touch, the door would open but then would be disabled until the touching wires were separated. Check out the wires themselves, the screw terminal connections at the opener itself, and at the switch to be sure there are no bare wires touching. If the wire goes through a concealed location to which you have access (such as an attic over the garage), look there too. Mice have been known to chew the insulated covers off wires!
You can, of course, check the continuity of the wires using a multimeter. Disconnect the wires from the opener and the switch, be sure they are not touching, and touch the probes of the multimeter across either pair of wires. If there is a resistance reading, then there is indeed a concealed short.
If the wiring is OK, you might want to change the security codes on the opener and remote. Maybe a neighbor somehow is activating your door. I have heard that even some radio transmissions, such as from airplanes, can also activate garage door openers… or is that just another "urban myth"?
Otherwise, my next guess would be that one of the circuit boards within the opener is defective, and will need replacement.
You must disable the garage door lock mechanism so that it cannot be inadvertently engaged. Accidental locking may cause severe damage to the door or the opener if the opener is activated!
Since you (or the next owner) might want to lock the door, don't do anything permanent. A bolt through the latch bar so it cannot engage in the track is fine. You may have to drill a hole through the latch to accomplish this. You may also use a small padlock instead of a bolt.
Since local building codes are so finicky, I wouldn't doubt that some areas might even require a "permanent" disabling of the locking mechanism. If you are concerned, check with your local building inspector.
I tried to search the FCC database myself. I can tell you the proper frequency for a freighter sending a distress call in the Mediterranean Sea, but garage door openers... forget it!
However, a knight on a white horse has come to the rescue. After sending out a distress call, I received this response from Karl Seidel of Aleator Garage Door Transmitters (now defunct, unfortunately). Aleator was an online supplier of replacement garage door remote controls:
"The range of different types of frequencies depends on a variety of factors: geographic location, manufacturer preference, etc. We stock and sell radio sets with the following frequencies (in MHz): 288, 300, 310, 312, 318, 340, 390, 434, and more; we commonly get inquiries from Canada & other countries that use other frequencies."
Unplug the opener, open the unit up and look inside. I am not familiar with your specific opener model, but from your description, I wager that this opener uses drive belts instead of gears or chains. This would explain whyit continues to run rather than stopping or auto-reversing. The belts are slipping.
Remove the belt(s), take them to a hardware store and get replacements. Clean all the pulleys with lacquer thinner or alcohol to remove any grease or oils before replacing them.
The fact that you are having problems at the limits makes me wonder if you may have some restriction in the door itself. Troubleshoot the door for resistance, check pulleys, etc. There are some good tips in the garage door article at the web site.
It depends whether or not the remote you purchased has that feature! Some remotes do allow you to open two doors, but the remote would have two buttons dedicated to garage door opener frequencies. Others have multiple buttons but they will only operate other features of Sears openers, such as turning on lights.
If you didn't get instructions or lost them, AAARemotes.com has instructions for many currently available openers, as well as compatible remotes for virtually every garage door opener. Their url is http://www.aaaremotes.com .