Any chance that the school's stopped allowing p2p use? Can other people use LW at school?

Delete 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. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.
In case you're using Vista: LimeWire Pref Folder in Vista

Had you updated Java around the time that LW stopped connecting? Try this Java version. Download the JRE offline installer & remove any other Java versions before installing this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

In LW tools > options > advanced > firewall config. Change LW's listening port to 64049 (or try others in the range of 49152 - 65535) > apply > ok.

If none of those work, please give us your details...it's hard to help without knowing about your setup.
System details - help us to help you