Fixed IP? At a university? That sound very unlikely. Ok, say it is as you say.
You can run "traceroute <IP_Number>". A staple command on just about any Unix or Linux system. This will get you back the IP numbers of all the "boxes" between you and the computer with that <IP_Number>. That is, if those boxes will respond. But even then, you would have to have some sort of knowledge of the network and where those boxes were. Sometimes the person setting up the network uses names that make sense. Like "comp_lab_2nd_floor". Other times they don't. Like "ciscio12394".
Next time consider installing a program that announces it's self. That way when the computer goes on line it will "say" where it's at. The best solutions use services which help track events even when you are not looking.
You didn't leave any back doors open. Say a telnet service or better an ssh service on an unusual port? Something so you could login when you saw it go on line?