As long as you're sure that your school hasn't started blocking p2p...

Make sure that the XP firewall is off & that ZA is configured to allow LW. For the free version of ZA check here.
ZoneAlarm Configuration - ZoneAlarm User Forum

For ZA Pro check here.
PortForward.com - Free Help Setting up Your ZoneAlarm Firewall.

Try this version of Java. Use the JRE offline installer & remove your current version of Java before you install this one (some people have had problems connecting with 1.6.0_01).
Java SE Downloads - Previous Release - JDK 5

If that doesn't help, try deleting LW's preferences folder when LW's properly closed. See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will kill all of your settings within options, you'll have to go back through afterwards & reset things.

When LW was working, did you see the firewall icon? You're using a wireless adapter, is there a router in your room/dorm that you're connecting through? Can you find out the brand & model?