Did you update Java around the time that LW's connection failed? Try this version instead. Download the JRE offline installer & remove your current Java version before you install this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

Have you always been able to use LW at work? If the port 6346 test doesn't work, something's blocking LW's default port. Talk to whoever's in charge of the internet there...find out whether there's been a change in the setup.

Lots of businesses won't allow p2p use...you need to be sure that your employers allow you to use LW while at work