This is really puzzling.
I dug out an old laptop which still has Windows XP on it. Installed ADE and Calibre. Pointed Calibre at the existing database on the server and got the same result - ADE doesn't open. I am sure it used to work but that would have been an older version.
I then analyzed what was going on with ProcessMonitor.
There are some very strange things going on when the database is on the server. It appears that Calibre is getting the path to the e-pub wrong then gives up trying to launch ADE when it can't find the file.
I have attached 2 logs, 1 for a network database and 1 for a local database.