OK--they are indeed confusing, but they will help track down your problem.

We need to find out why LimeWire is quitting when loading.

Console will (I hope) give an error message when you try to open LimeWire.

Console is in your Applications folder inside the Utlities folder.

Could you open Console, and then try to open LimeWire, and then note what messages are shown in the Console?

You can post the parts here, or PM me if you preferr.

Cheers