I don't know why this worked but....as I was in the middle of downloading the UnInstaller recommended by Brian, I decided to try one more thing.

I went to explore my C: drive, and went into LimeWire Shared file, where the songs were located. While in there, I was actually able to MOVE the songs to a new folder I made under the Shared folder. Once they were moved, I went into the new folder, and could delete them from there.

I tried moving them before while in LimeWire and couldn't. Like I said, I don't know why this worked, but I'm glad it did. Thanks for the ideas and the quick response! )