FolderBrowserDialog will always popup at the Server side, the client/browser will never see it so client would hang there forever waiting for input...
In your case, both Client and Server on the same pc, this is why you saw the dialog working. As far as I know there are no components from Microsoft that allow to browse the Folders on Client side. But you can always try open source Solutions...
for instance: http://www.codeproject.com/Articles/21895/Directory-Browsing-in-ASP-Net-2-0