One simple test you can do is to point the IR LED of the remote at a digital camera or video camera lens, and look in the camera viewfinder to see if it flashes.  It should appear as a fairly bright light.
Jeremy wrote:

Is there any reason other than a hardware problem why my DVICO remote
would have stopped working when everything appears to be configured
I'm thinking I might have to physically take the remote apart and see if
I can see if there's anything awry, unless there are any other ideas?