I'm using the 2.4.4 client of Limewire Pro. I was
downloading a very large file. The remote server probably signed off, after a while and I was left with
a half-finished file. I killed the download and
the half inished file is in my incomplete folder.
When I do a search and I see the same exact file
again with the exact same, how can I make it continue and connect to the
file that I've already have half downloaded? Mind you,
the semi-downloaded file is not in my "downloading"
window, on the bottom of the screen, but only in my
incomplete library.

You should be able to select a file with the same name and size and start downloading it again and LimeWire will pick up where it left off.