perhof:
It sounds like you're stuck on trying to open some shortcut on your desktop which would probably work in a native Windows application but with Java... nah.
Do you know where your dropbox folder is located?Mine is at C:\Users\username\Dropbox in Windows 7 and if I browse there from the Arduino IDE open dialog I can open the sketches.
If you find that path hard to browse to you could create a symlink to your dropbox folder somewhere elsemklink /D C:\Dropbox C:\Users\username\Dropbox
Perfect - navigating the long way works (and I didn't think of this why? )
Strange how desktop shortcuts open fine in the Mac IDE.
Cheers!