I was hoping to find out if there was a way to connect to the bitcoin network when you are in a network with only port 80 open.
If your outbound connections aren't so strongly limited, then you should be fine. Bitcoin server can work good enough even if other peers cannot connect to it. It will initiate connections and "stay in the business".
And even if you want peers to be able to connect to your node inside your lan, there's usually the option of setting up port forewarding on your router.... unless the OP isn't on a network he/she can manage (but, for example, on a corporate network)? @OP: could you tell us what you want to achieve and wether or not you're on a home network you can manage, or a network that's managed by somebody else?