Limewire was having difficulties connecting so I followed the proposed suggestions on the webpage that said to delete Limewire completely and re-install it. However, after the reinstallation when I try to open Limewire a screen pops up that says: You can't open the application "LimeWire" because the Classic environment is no longer supported.
Can someone explain what this means and how I can fix this??
Please and thank you.

Classic environment means pre-OSX. Generally OS 9. So no, the OSX LW will not run in OS 9. You need one of the more recent LW versions depending on your version of OSX. You are obviously not running an intel mac, so you would be unable to use LW version 5.
See which version suits you here: Lime Wire » Download Out-Of-Date Installers
For OS 9, choose the classic version.

Thank you so very very much!!