Technically you don't need a second NIC to set up a proxy server, you need a second network connection -- NIC is just the easy and sane way to do it. Any hardware which you can finagle into talking from one computer to another can act as a network connection if you spend enough time (but not money) on it. Might not be particularly fast, or stable, or useful, but will give you a much better understanding of networking in general.
In lieu of a proper NIC, and hardware permitting, I would look into PPP over Bluetooth.
Of course, that's assuming I really really don't want to spend the $5-10 on a new card.