When you say that the C drive is inaccessible, I take it that this means you can't install software to it? Windows Live Mesh is very good, but requires an installation to both ends. You're going to need a web based service from the sounds of it. Something like Logmein which requires installation on the computer you want to access (which, being your home computer, shouldn't be an issue). You can then log in from the other computer via the interweb - there's a free version and a pro (differences are here). I haven't used it myself (am a Mesh fan) but have heard it's very good.
SSH tunnel with Putty on your USB stick *might* do it. You'd need to set up an openSSH server at home, preferably a separate server to the one you want to connect to. As mentioned before, you could use VMware Server to host a second box on one of your real servers.
You can not access the C:\ drive at all, it's locked down. Isn't in My computer and making a C:\ shortcut, run etc just give an access denied. I can install something on my memory stick and then run it off there if that'll help? Logmein looks ok if it isn't blocked at work, but you can't transfer files.
logmein pro allows you to transfer files, dropbox would work as well. You could port forward 3389 at home & remote desktop to a machine but the port might be blocked at work
I actually use the free edition of logmein.com and it works brilliantly. Also i would check out teamviewer.com it also works quite well and is free for non commercial uses.
It'd have to be a Free option, is RDP secure over in internet? Is logmein better than teamviewer, can you transfer files with teamviewer. Is SSH, VNC an option?
Putty is standalone and will SSH tunnel. You can then use the standalone vncviewer.exe to connect to your PC via the SSH tunnel. Or that's the theory anyway!