Unless I'm misreading this - I don't think you understand how the remote
stuff works.
Too make the connection you need to have a client side and a server side.
Most people want the client side to be their house so they can connect to
their work computers - the server side. In your case - I thought you wanted
to be able to work from home on the university computer?
If so - and providing you won't get into trouble - install Go2MyPC server
(very small program) on the computer at school you want to connect to (there
is a fully functional free trial period). Then from home, or from any web
browser from any computer anywhere in the world - log onto
www.go2mypc.com
and log on and you will see your school computer - which you will be able to
log onto and your client screen will appear as if you are sitting in from of
the school computer.