to make it a little simple than MexicanOnABike, you could find the IPs easily enough by
- going to "My Network Places" (should be visible from the start menu)
- clicking the "View Network Connections" option in "Network Tasks"
- clicking on the "Local Area Connection" in the main window
- looking at the IP displayed under "details" on the left
So if your IP is 192.168.1.20, you can go "Start" and "Run" and type in
\\192.168.1.20\c$
and you'll be on the root directory of your C drive.
edit: if you actually do the copying FROM your machine (i.e. drive the copy from your machine) then it really comes down to the security setup on the desktop. So find out Grancey's IP address and then do the start/run thing above from your laptop.
You know - the other alternative might be to borrow an external (USB) drive from someone (something big enough to fit the files onto it).