I wanted to go ask the guy at the computer department if there was anything in place to prevent my laptop from seeing my PC, but I don't quite know what to ask him.
My laptop is on wifi, and I bought an ethernet cable for my PC. Both have dynamic IP addresses through dhcp.
If the hostname of my PC is george, and the hostname of my laptop is frank, and I use the user 'owner' on both, I should just be able to be in my laptop and type this, right?
owner@frank:~$ ssh owner@george
but I get nothing. I've also tried to ping my laptop from my PC and vice-versa.
Is this because they are on two different interfaces, or is it because the department is blocking something, or do I need to do something to have these two be able to see eachother on the network?

- of course you'd get nothing - how would one machine know hostname of another or behind what ip address that hostname sits! For static IPs on a small network appropriate entries in /etc/hosts file would be enough (see 'man hosts'). Alternatively you need a name server.

But if your IPs get assigned dynamically and it's a big network that you cannot ask for any favours (for instance, you could have asked to have DHCP server reserve IP addresses for your machines based on their MAC addresses) you can just check your current IP address, keep the machine connected and hope that that IP stays reserved for a reasonably long time (ask network admin how long). When I used to have dynamic IP from my ISP my address sometimes didn't change for weeks as long as I stayed connected.