I am a university student who, from August to May lives in a dorm room. There I have a capable internet connection. However, as I have strong ties to my home two hours away, I go home most weekends. I would love to be able to ssh into my desktop at school from my laptop at home, but currently cannot.

The school network assigns internal addresses, then essentially proxies us through to the internet. That is, the rest of the net thinks I have one IP address, but every student computer (or at least many of them) share that IP address. I can connect from my school computer to a home computer, but not vice versa. To add to the trouble, my home IP changes frequently.

The desktop is mine, and I am root on it, so I have its full cooperation. The laptop is mine and I am root on it, so I have its full cooperation too. Is this enough to whip up a hack to let me into my computer?

You could use a dynamic DNS service to get around the IP address changing on your home computer.

I use a SSH tunnel to make a quick easy VPN between computer A and computer B, and when I get home I can ssh back through the tunnel.

Alternatively you could use VPN software itself.

Either way have a script that reconnects if the connection is dropped.

I must admit that I am unfamiliar with vpn's and their associated software. The laptop moves with me back and forth from college to home, so it does not have a continuous internet connection. Therefore, when I want to connect the two computers, I only have physical access to the laptop, and the desktop has no knowlege of the IP address at which to find the laptop. This issue isn't important enough to me that I would pay money for a dynamic DNS service.

I'm thinking of a hack involving putting the IP address on a free geocities web page. I can write a script for the desktop to run as a cron job, wherein it checks that page for an IP and if it finds one attempts to create a vpn with it. Then, I should be able to remotely login via the VPN, right?

And on an ethical note: the university is not trying to prevent me from doing this. Attempts to block such connections are intended to curb music and video piracy, not students remotely logging in. I have read the terms of usage, and this is within them.

Did you contact the system administrator. Maybe they already have a setup for this and they only have to enable an option on your 'account'.

most unis will gladly forward port 22 to you if you ask tehm politly for it and state your reasons

the other option is to run nmap on your uni from home,
then try moving your sshd to one of teh ports that are open, (if any)

I'd say that getting a 'free' Dyndns.org dyndns.xxx address assigned to your school computer address if possible is the route to take, (the admins at the school are probably 'PAT-ing' those connections (may be a tough on), or 'NAT-ing' them (possible) and a good idea is asking the admin or figuring out what port can be forwarded to that machine within the school network from any address through their firewall. Some will allow port 22 ssh traffic, some will assign another port for that purpose, ie. :8022.
You may have some proxy info that the admin can provide as well that may be helpful, it can't hurt to ask the admin staff, or try the nmap route but watch you don't get yourself into hot water with that method.

hamachi is your friend.

http://www.hamachi.cc/download/list.php

enjoy. this will bypass the schools firewall and NOT get you in trouble. plus it is free.