When I try to share the unshared (red) files in my Incomplete folder, the option is grayed out. I also cannot access the details of these files. The files exist. I use the option to share partial downloads. Thanks.

You should NEVER share incomplete files directly. People cannot use incomplete files per se. How it works is you turn on 'Allow Partial Sharing' via Tools -> Options -> Sharing -> Advanced. Much of downloading on the gnutella network includes partial file sharing. When you download a file from many hosts, chances are at least some parts of those files are from people who are simultaneously downloading the same file. Parts of those files are shared. However this process can only be done whilst the above option is enabled.
... a protocol for sharing partial files on the Gnutella network. A partial file is a file that a host has only downloaded parts of. Partial File Sharing allows files to spread faster over the Gnutella network.
After enabling Partial File Sharing, only new downloads will become partially shared & not be red in color. It looks like at some point you had Partial File Sharing disabled, else your incomplete files refused to load into the download window at some point. I would not worry about the incomplete files which are red.

The last reasons I can think of why 'some' incomplete files might be red is, (a) Days to keep incomplete files, has passed. This setting is under Tools -> Options -> Saving. (b) The incomplete file is a duplicate, the original forgotten about by LW, perhaps the file was later downloaded using an alternate incomplete file.