Don't run more than 1 software firewall at a time. Choose the one you want to use, make sure it's configured to allow LW & disable any others

Some people have had connection problems with Java 1.6.0_02.Try this version instead. Use the JRE offline installer & remove your current Java version(s) before installing this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

If that doesn't help, If that doesn't help, delete LW's preferences folder when LW's properly closed. See point 2 here & also point 3 if you've used newer versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will kill all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.

What happened when you did the port test (#10 in the 'system details' list)?

What's the model of your Motorola? Is there an external router (not the Realtek ethernet controller)?