It's a long shot, but you might try opening a new email. Click signature from the ribbon menu at the top. The drop down has a link that launches the signature window. Maybe accessing that window from a different place will cause it to launch.

Beyond what we've already discussed, I'm kind of shooting in the dark. A registry repair might be helpful. An online update and repair from MS might be helpful.

Anyone else have an idea of how to repair Outlook for this?