This would depend a lot on the university. Quite a few allow journal article access via login
If you have SSH on your university system, and can SSH into it, you could use ssh tunneling between the systems - between linux systems, as i understand it, should be as simple as
ssh -ND 9999 firstname.lastname@example.org on the client side. D allows for dynamic port forwarding, and N opens no prompt aside from the initial password.
You will then set up your web browser to use a socks proxy at port 9999, and set up your web browser to use the DNS server on the proxy side by going to about:config and setting
network.proxy.socks_remote_dns = true.
Instructions adapted from lifehacker
This will allow you to connect using your local browser, as your university computer, which should allow full access to internal university resources.
You can do the same from OS X. For windows, putty will act as a client.
If you have more control over the server, and want a slightly solution that is running all the time without needing to log on, you can set up tinyproxy - It dosen't have password authentication so you'd need to set it to only serve to your ip address, but i found it was a simpler solution for me to set up.