You could remote twice.
Connect Infected computer to another computer via a router on it's own IP range.
Connect the other computer to the University network (it would need a second NIC).
Remote into the other computer, then use that computer to remote into the infected computer. As long as the "other" computer doesn't have a way to easily get infected, it should be fine.
I'd put Linux on it just to make it that much more unlikely. Hell, you could even put Linux as the Host OS on the "other" computer, then put Windows as the Guest OS. Then only allow the Guest OS (Windows) to access the infected computer.
So the process would be like this:
- Remote to Linux other computer.
- Open Virtual Machine with Windows on it.
- Remote to infected computer through the VM.
This would adequately keep the infected computer on a separate network. Note you would only allow the second NIC access to the guest. The host shouldn't be able to use it.