The FolderBrowserDialog
does allow me to browse computers on the network, but it displays other unnecessary folders (I don't want local folders). Also, I don't want to have to select a folder - just the computer name.
Found the answer:
The ComputerBrowserDialog
http://discoveringdotnet.alexeyev.org/2008/04/how-to-browse-for-computer-name.html
I tweeked it a bit to behave more like the FolderBrowserDialog (only took a few min). Works just how I want it to.