Just as a test I tried doing a clean install of the newest JAVA and Limewire basic to see what the fuzz was about and had no problems what so ever getting it to run

Over 3 years old Laptop.
1.7 GHrz Pentium 4.
224 MB Ram.
52 MB Ram integraded videocard
Windows XP Pro (Service pack 2. Automatic updates. Ran the patch in Download/Upload problems)
Limewire 4.12.6 basic (Offline install)
Java 5.0 update 8 (Offline install)
AVG Free Antivirus
Ewido Antispyware
Sygate personal firewall