the windows XP remote desktop thing works fine...
if you have XP pro, right click on the my computer icon,
now go to the rempte tab, and enable remote access...
now at work just use the remote desktop connection tool, (start>programs>accessories>communications>remote desktop conection).
OR...
get VNC (
www.realvnc.com)...
(you can make that work with port 80)
Getting firefox and a proxy will do nothing more than just changing the proxy setttings in internet explorer, so that's a bit of a non-starter really...
Of course all of this will only work if it's set up to be allowed to work.
Most firewalls will also have attached Proxy servers (and it's the proxy servers that are doing the filtering).
So you can only access the proxy server (that's your gateway). and you can only access that on a proxy port (8080, 3128).
only the proxy server can access the internet on port 80.
e.g for any of these ideas to work you're giong to have to get the proxy server to proxy non http packets, (which it won't)...
if they work get your bosses to give me a call and I'll come and show them how to secure the network properly!