That's very poor news that you can't reach the 6346 test page. Might I suggest you try another listening port. eg: go to LW's menu Tools>Options>Advanced>Firewalls & type in 4915 & select Manual force ip & type in the same no. Press the Apply button. Then go to menu, File>Connect & give it 15 mins or so. If nothing happens go back to File>Disconnect, wait a minute, then repeat the process.
If this doesn't work for you. Then I don't know if this will work but it's worth a try by setting up a proxy.
A Fix for those whose ISP's block Limewire which is using proxies. Also go to page 2 of that link & find the other link for more instructions on how to do it. Good luck!