Be patient, nobody's forgotten about you

Which Java version did you download? Try this one. Use the JRE offline installer & remove any other Java versions before you install this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

Looks like your router has a firewall. See the link below.
http://www.timewarnercable.com/Media...20Benefits.pdf

But...I can't find specific instructions for port forwarding (to get rid of that firewall icon). If you have a user manual that came with your router (I can't find one), look at the instructions for port forwarding.

Try changing LW's listening port to 64049, or something in the range of 49152 - 65535 (in LW tools > options > advanced > firewall config. Click Apply to save a change).