Win 2003 Server copy/paste problem

Try instead:

shutdown -r -f -m \\hostname -c "Comment goes here"

That's a bit drastic, but I've had the need to do that in a very similar environment to what you describe. I also open a cmd window and start a ping -t against the server to watch when the IP stack goes down and comes back up. This is a very useful indicator of activity when you don't have physical access to the server (or are too lazy to get up and walk over to it).

EDIT: (based on your comment) Ok, do this first and then try the above again (or restart it as normal if this works). See it that gets you farther. The -a will abort a system shutdown.

shutdown -a -m \\hostname

To the best of my knowledge, clip-board sharing does not extend to files just to text blocks. So it is possible to copy paragraphs between your host computer and the RDP session, just not copy and paste files. This is because the clip-board does not store files, per se, it just stores data.