For Windows 7, you must set Java to Run as Administrator ! Otherwise it will have difficulties such as connection problems. I also incurred the same problem at one time.

Since LPE seems not to run with the newest Java 1.7 which I suspect is really a beta, it will probably be easiest for you to reinstall Java 1.6.

Right-click the Java 1.6 installer & choose 'Run as Administrator'. You may need to reboot after installing I'm not sure. Download the safer 'Offline' Java Installer For Windows: Java Downloads for All Operating Systems.

It would also not hurt to do the same for LPE, right-click the short-cut on desktop for LPE & choose Run as Admin. when you get to that point.