UNIX for Dummies Questions & Answers

If your behind a router you will have to make a route through it to get to the server.

Not the same thing. You use the ssh client from your Ubuntu box to connect to your school server, which is running the ssh server daemon in order to accept ssh connections.
That doesn't mean the ssh server daemon is running on your Ubuntu server unless you specifically installed it after you got your Ubuntu box up and running. I made the same erroneous conclusion at one point...found out ssh server was a separate install.

Next question...I see Ikon assuming your Ubuntu box is not on your local network connected to your router. Is that the case or is your Ubuntu box on your local network?

My assumption what based on this comment....

But that was assuming that both PC's, as you said, were on different subnets.

I just went through this myself, built a HTPC for the living room. nixnoobb hit it, you have to install shh server (sudo apt-get install openssh-server) start it (sudo service ssh start) then enable it at boot up (chkconfig ssh on).
You will have to use the system ip (192.168.1.103) until you get it setup with a static ip.
There are a lot of "standard" services that are not installed with ubuntu that you have to manually install. I guess they do this to keep the initial install very small. I had a hell of a time trying to mount my servers (solaris) disks. Turns out NFS of all things was not installed!

behind a router, I mean they all on the same router. modem > router > linux and vista box. Sorry for the confusion.

But I installed ssh server and now it works.

Thanks for all the help.