Thanks for all the replies!
David, your script certainly looks like it could work. I need to check if it's a certainty that every PC accessing the site can be named this way.
I also came across this thing that has a completely different
way of solving the problem.
http://www.mvps.org/vbnet/index.html?code/network/macaddressremote.htm
Now I've just got to figure out how to call it!
Thanks again.