I have recently found issues with a couple of Access database shortcuts which don't appear to do anything when you double click on them. In this particular instance it's Access 97 running on Windows Server 2003. After a bit of investigation it appeared that the issue is with file association.
The Access shortcut doesn’t work because it requires reference to MSACCESS first. You would find that you could open Access first and then open the DB file. In this case the shortcut must include the full path to your specific Access executable, and the DB file. Therefore a quick workaround is just to do the following:
Right click on the shortcut on your desktop, then go to Properties. The shortcut's "Target" box should be something like this:
"C:\Program Files\Microsoft Office\Office\msaccess.exe" "X:\Shared Company Data\Subfolder\YourDatabase.mdb" (The latter part obviously being your specific path to your database file).
Hope this saves someone some time and headaches!