Alright, I've double-checked with the network guy for my school:
The subnet mask should be 255.255.254.0.
I set it to that, but again, nothing.
I did a lsmod to see if the module for the card is loaded: it is.
Physical connection is properly in.
It is a regular ethernet cable.
The broadcast has been changed to 126.96.36.199.
The same NIC was working under Slackware 8.1 on the exact same computer earlier. I had to reinstall Slack for other reasons, and now I'm at this point: everything besides the network interface working.
The cable was working before, but I tried a new one anyways. Still no good.
I wasn't able to ping the gateway, but the other people on my network could.
So, yeah. Still no idea what it could be.