You can buy Amazon AWS, or any VPS, or web-hosting with SSH access, and use it's IP to browse internet (and for Tor outgoing connections). If you'll have SSH access to any computer outside your campus network, the rest is given by SSH Tunneling (
ssh -D) technique. Google
Tor over SSH Tunnel, - that's how you can run Tor 'as it is running on IP of your hoster', and use it from your home computer.
The other way could be
Tor bridges. We need to know how exactly Tor is blocked in your network.
What is the program you have to enter your username/password before accessing internet? Is it like web-login or like VPN Client? What are your network settings after you get connected? And what is shown in Tor error log?
