Wow, they let you open ports on the router and firewall but you can't install software on your PC?? That seems silly... We technically have a policy saying no installing anything even for those of us that are admin types but they realize that there are just some tools we need to have... Do you have a good work justification for wanting to get to your PC remotely? If you asked would they let you install VNC if you have a good reason?
(they're not too bright here) but yeah, I think I might be able to justify to them why we need this and get them to let me install it.