For Windows 7, you MUST set Java to Run As Administrator. Otherwise LW will not connect. You can achieve this easily for LimeWire by right-clicking the short-cut on desktop. But for Java, it would probably be easier to reinstall Java 1.6 (Java 6). Right-click the Java 1.6 installer and choose Run as Administrator. See how things go for connecting after that.
Download the Java 1.6 installer and then follow the prior instructions:
Direct Java offline download link
(Please note, LW5/LPE do not run with the present version of Java 1.7.)