A .epub fiole is a zip file in disguise ... it looks as if your default opening program is the wrong one.
First check if you can open the .epub files from Digital Editions (ADE) by drag-drop onto ADE, or by File/Add to linbrary (ctrl-O).
If that is ok, associate .epub files with ADE; might be easy, sometimes awkward ...
Sometimes the registration of ADE to Windows as the default hander for .acsm and .epub files does not work;
that is what causes the double-click in Explorer to fail;
especially in Windows 8/8.1, and maybe 7;
this appears to be a bug in Windows (for once not a bug in ADE).
Two possible ways round it.
First, try to force it in Explorer
Right-click on a .epub file (and repeat entire sequence for .acsm if necessary)
Select 'open with' if on the list, 'open' if not.
Select 'choose default program'
Select ADE if it is on the list,
If not select 'more options' and navigate to the ADE executable (may be at C:\Program Files\Adobe\Adobe Digital Editions\digitaleditions.exe)
Now .epub/.acsm files should be associated with ADE, and double-clicking should work.
Sometimes, Windows allows you to go through all that, but then refuses to make the association you have asked for.
In that case, the only way I know is to use a third partly file association program.
Thanks so much! Forcing it in explorer worked. When I exit the ebook, it vanishes from my library, but at least I can read it now. I'll try your other suggestions to fix that issue. Thanks very much for your help. DS.