I guess I'll take it down and open it up to see if there's something I can fix inside, but I'm not optimistic. I looked around the 'net a bit and it seems that parts for this are no longer available (not surprising.) I'm not upset - this thing has lasted about 25 years with daily use and never been maintained, so I guess we got our money's worth out of it.
What I'd like to know is, can I buy a replacement opener that will work with the existing chain? It would be a lot easier to replace just that unit than to have to replace the chain, springs, etc.
So, any advice about this? Here's some pictures of the old unit, and a parts diagram I found on the Sears web site.