Step 1: contact your school's IT people. You could be running into a situation where only specifically authorized computers are allowed to connect to either the wired or wireless network.
Step 2: what does the Network Preferences pane say for DNS servers on the wired and wireless adapters? If these are blank or something that starts with 169.x.x.x, you're not getting DNS server information when you connect, and without that, you'll never connect. Here's a quick thing to try: when your machine says it's connected to the school's network, enter 207.58.150.187 (the IP of these forums) in your browser address box and hit Enter/Go/whatever. If you wind up here, it's almost certain that you're having a DNS problem. If not, there's something else going on. This would be good information to have when you talk to the IT people, too. "I can get to web sites when I enter their IPs, but not when I enter their URLs" or "It doesn't matter if I enter a URL or an IP, I don't get anything."