How did you uninstall LW? Don't uninstall via add/remove programs, that can cause problems. Open task manager, check whether there's a LW process running. If there is...end the process. Use your computer's search to look for all files & folders with LimeWire in the name & delete from there. The correct way to uninstall LW is via start > all programs > Limewire > use the uninstall option. Also, installing a new version of LW will automatically uninstall the old one.

When you do reinstall LW, install Java first. Use the JRE offline installer & remove your current Java before you install the new version.
For Windows XP, try this version: Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11
For Vista, this latest update seems to work for most people:
Java SE Downloads

Once Java's installed, download LW using it's offline installer. When you click to download & the download box pops up, ignore it. There's an option to use the offline installer within the orange box on the download page...use that one.