As you know,electronic door openers are most often pretty reliable. I have a similar set as you describe. Still working after 20+ years. Sears. Here's a few things I have discovered:
If the lite on the remote comes on the battery is good enough to drive the transmitter.
If the light doesn't come on the battery connection is usually not making up. Silicon grease on the batt. terminals seems to help. A new batt. may help.
If the remote is transmitting; And door doesn't work,The little wire antenna may have fallen off the actuator or be wrapped around a metal brace.
Mine have a door lock button on the wall unit. If it is depressed the door won't oprate from the remote.
Cold weather will cause the tracks to bind. The door will refuse to go.
I have before closed my door and when I came home they were open. I found the 'down force' pot was on the 'edge".
The door had closed and returned to open. I had driven away without noticing. Track binding or dog caught under door. Some doors have safety devices that will prevent operation if they become misadjusted.
For doors to work well the door springs must be adjusted for zero weight. Unclipe the track latch. The door should move with finger pressure and stay anywhere you put it.
Sometimes the door guides need lubricated. Or the old lube has turned to gum. I found some salt water grease that woorks well. The little wheels are tough to clean. Not a white shirt job.
Have you ever been around when one of the springs, mine have coils, break and fly past your ear? Make sure the springs are tethered.
They usually break when you are ready for Sunday School.
Mine have relays in the transmitter. You can hear thm click if the remote is transmitting.
I hope these little thoughts will help.
I am eagerly waiting for a UFO to come an give me a ride.
Best Wishes.
Ivan Copas

Homeowners up in arms: U.S. military frequency jams hundreds of garage doors
ASSOCIATED PRESS - By Robert Weller - December 3, 2006 -- DENVER -- What do remote-control garage door openers have to do with national security? A lot, it seems.
A secretive U.S. air force facility in Colorado Springs, Colo., tested a radio frequency this past week that it would use to communicate with first responders in the event of a homeland security threat.
But the frequency also controls an estimated 50 million garage door openers, and hundreds of residents in the surrounding area found their garage doors had suddenly stopped working.
"It would have been nice not to have to get out of the car and open the door manually," said Dewey Rinehard, pointing out that the outage happened during the first cold snap of the year when temperatures fell well below freezing.
Capt. Tracy Giles of the 21st Space Wing said air force officials were trying to figure out how to resolve the problem of their signal overpowering garage door remotes.
"They (military officials) have turned it off to be good neighbours," he said.
The signals were coming from Cheyenne Mountain Air Station, home to the North American Aerospace Defence Command, a joint U.S. and Canadian operation set up during the Cold War to monitor Soviet missile and bomber threats. ...

:Homeowners up in arms: U.S. military frequency jams hundreds of garage doors
:ASSOCIATED PRESS - By Robert Weller - December 3, 2006 -- DENVER -- What do remote-control garage door openers have to do with national security? A lot, it seems.
:A secretive U.S. air force facility in Colorado Springs, Colo., tested a radio frequency this past week that it would use to communicate with first responders in the event of a homeland security threat.
:But the frequency also controls an estimated 50 million garage door openers, and hundreds of residents in the surrounding area found their garage doors had suddenly stopped working.
:"It would have been nice not to have to get out of the car and open the door manually," said Dewey Rinehard, pointing out that the outage happened during the first cold snap of the year when temperatures fell well below freezing.
:Capt. Tracy Giles of the 21st Space Wing said air force officials were trying to figure out how to resolve the problem of their signal overpowering garage door remotes.
:"They (military officials) have turned it off to be good neighbours," he said.
:The signals were coming from Cheyenne Mountain Air Station, home to the North American Aerospace Defence Command, a joint U.S. and Canadian operation set up during the Cold War to monitor Soviet missile and bomber threats. ...

:Hi. I have read similar reports. I have never been troubled by this sort of thing.
I have two garage doors with separate openers. They never seem to interact. There are dip switches I set differentlly for each door. Perhaps the government testing signals don't get to southern Ohio.
I'm not sure how the coding works. My units work up to a distance of about 1000 ft.
Best regards,
Ivan

That's the same kind I have (Delta 3 from Linear Corp))
http://www.linearcorp.com/radio_control.html
with dip switches that work on about 310 mhz
http://www.linearcorp.com/pdf/manuals/dnr00001.pdf
..and the range for mine is usually only about 100feet or so... but my garages are below ground under the house.

I am located in north jersey in the NY/NJ metro area about 15-20 miles nw of manhattan

And what ever radio signal it was that knoced out my remotes was rather strong.... and lasted at least 1/2 hour.

http://www.aaaremotes.com/fccpunoforga.html
http://www.aaaremotes.com/racoupki.html
http://www.aaaremotes.com/misimayjamga.html

:http://www.aaaremotes.com/fccpunoforga.html
:http://www.aaaremotes.com/racoupki.html
:http://www.aaaremotes.com/misimayjamga.html

: Hi. I have often wondered what frequency these things operate on. And how the dip switches identify the different remotes. I live on a farm about a 100 miles from Cincinnati. The strongest signal I get is WLW AM. I would suppose thaat a signal of high enough level very close to the remote frequency would confuse it all. I wish now that I had saved a frequency analyzer from the old days. Most likely none were high enough range.
I devote about half a day each spring to cleaning the tracks and pulleys I have. I adjust the springs for tension and make sure they are tethered well. I have had several break. I have three cars stored in this building. I'm sure a flying spring would take out a windshield. Not to mentiion my nose.
I enjoy all of your posts. I always read them when I look at my mail. I always learn something. And it's always fascinating to hear how others think about electro mechanical things.
Best Regards,
Ivan Copas

I called "Linear" the manufacturer of my Delta-3 remote door controller today and they told me that my info about the situation and the formall FCC announcement back in 2005 was the very first they had heard anything at all about this situation even though it was announced by the FCC back in 2005!!
The info I read from the FCC indicated that the military frequency is at 390mhz... and my controller oprates at 310mhz.
Anyway "Linear" said they had no prepared fixes for this item and all remotes they make work on anywhere from 310 to 390 mhz
So I called another place that advertizes fixes to solve the problem. These people told me that if my remote is set for 310mhz I should NOT be getting the interference from the military frequency at 390mz.
So they think that maybe it's from another culprit like maybe a remote controller for a model car or airplane etc. Maybe even some kind of computer wireless gear like maybe a wifi something or a wireless signal-router of some sort...
But they could only take wild guesses too.

So Now I have to see if and when this ever happens to me again to see how much of a problem it turns out eventually to be.

Door Springs:
I too have had the springs break several times and the end pieces came blasting right past my head like a missile or a bullet!!!
Scared the crap out of me.
I bought tethers for the new springs now but actually never installed them yet...lol
....living on edge I guess