It appears your DHCP setup is not working.
You don't have an IP address assigned. Look at your ifconfig output for eth0. There is no "inet addr:" listing. Nor "Bcast:" or "Mask:" Those should be assigned to you via DHCP. The line of ifconfig output that shows this data normally is the second line, between the lines that start with "Link encap:" and "inet6 addr:"
Here's my eth0 listing from home. You can see my IP address there is 192.168.0.52, shown on the second line of the output:
eth0 Link encap:Ethernet HWaddr 00:E0:4C:D4:31:D1
inet addr:192.168.0.52 Bcast:192.168.0.255 Mask:255.255.255.0
inet6 addr: fe80::2e0:4cff:fed4:31d1/64 Scope:Link
UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
RX packets:544858 errors:0 dropped:0 overruns:0 frame:0
TX packets:379809 errors:0 dropped:0 overruns:0 carrier:0
RX bytes:536689070 (511.8 MiB) TX bytes:62887456 (59.9 MiB)
First, I'd determine if you've got something messed up in your router (is is filtering/denying DHCP requests?)
Remove the router and plug your computer directory into the school network. Do you get an IP address assigned under that scenerio?
p.s. - It would be good to make sure your computer is secure and has iptables running and stopping unrequested incoming traffic before plugging directly into the school's network. Alternately, you could just boot with a LiveCD (Ubuntu can boot directly off CD) and run the DHCP testing that way. So you won't expose your harddisk install of Ubuntu to hacking or compromise. Once you figure out how to get an IP assigned in the LiveCD mode, you can go back and get things going in a firewall-protected harddisk-boot mode. Linux is not as likely to be quickly compromised as Windows, but the possibility is still there, so don't do something with a direct network connection before thinking things through.