Dare I say it but that test page seems to be down. lol
OK let's try this:
1. Try deleting your LW Preferences folder whilst LW is closed; instructions here:
Fixes for Limewire
2. After opening LW you will need to reset your options, but leave everything at default except the following: Go to Tools>Options>Connections & untick connect on startup & press apply button. (Also go to Tools>Options>advanced>Startup & make sure connect on startup is unticked.)
3. Go to LW's menu File>Disconnect. Wait a minute. Then go File>Connect & wait about 10-15 mins. to see if it connects.