I would like to run a Ubuntu server (in server mode; which doesn't have an X display) and access it via VNC. when I try to start the vnc server it complains about X not being there. Is there a way to run ubuntu (on a single board computer) without X and access it via vnc??

vnc requires x, you can't access a desktop that doesn't exist.

however you can use putty and login via ssh. (or any other ssh client)

Yeah... you wouldn't want VNC for using only console-related tasks. Putty + SSH make a good combo

I could also recommend to you webmin for doing admin tasks.