After connecting to limewire, the connection fails. I do not know what to do. Please help!

Assuming you are using some flavor of Windows here is a test - if not using windows the method may change the concept is the same;

Your ISP may now be blocking traffic on port 6346 - If that is the case you might want to try using Telnet to test your ability to connect to Gnutellanet. You can test this by clicking
Start
Run
"telnet 64.61.25.171 6346" (everything inside the quotes)
Enter

A window should open with 'Gnutella OK ' in it ... if not then you are most likely being blocked somewhere down the line with the most likely culprit being your ISP at that point I would contact your interent service provider and ask if they are blocking port 6346