Why can't you download stuff at home?

Why are you using your own computer on the company network?
Is it to save them cash having to buy you a computer? If so perhaps they'd be willing to come to some kind of compromise over the network access; maybe their concern is that you're downloading non-work related stuff and wasting time playing games instead of working, so perhaps they would allow you to have derestricted access outside work hours or something.

Sorry to be the "boring" voice suggesting negotiation rather than trying to help you defeat network security but (a) if your sysadm can't prevent you technically they'll HAVE to resort to firing you, (b) if you're responsible with corporate resources instead of trying to "hack the man" then you'll become known as someone who can be trusted (and therefore given more responsibility, which means more $$$, which means you can afford your own IP connection at home) and who can be worked with.