I had the problem of LW not connecting With Windows 7 before I upgraded to 8. I was wishing that the Upgrade would solve the Problem It did not.
I am still trying to figure out how to use windows 8. So any help as to how to set Java to Run as admin. would be a great help. the Java is Java (TM) 6 update 27 (I also have) Java FX 2.1.1 in my installed Program Folder

OH I Uninstalled the Antivirus to find out if that was the cause. it is not. I checked the Windows 8 Firewall and LW is approved to get thru

Did you try setting up a test account? If unsure how, just ask.
In the test account, disable all security software which includes spyware, firewalls, adware, etc. and see if LW connects. Also install FrostWire and see if it connects in the Test account.

To set Java to Run as Admin. Go to the Start menu search box and type in java.exe and it will show under programs. Right-click and choose properties and compatibility and check option to Run as Admin. I don't know if it's necessary but you can also right-click and choose Run as Admin after that.

I worked it out The Windows 8 Program does not have Java installed in it. I had to do a Clean install of Windows 8 and then Download the "OLD" 6.0 Java and install it. In order to get LimeWire to Work

Great to hear you solved the problem. I presume LW is now connecting.
By default Apple are no longer shipping their OSX with Java. Not sure about MS but sounds similar with Windows 8. This is apparently due to security issues with Java. I posted a link to a blog about this in the LPE thread I think it was.