I meant to update this, but got very busy this morning. I figured it out. I noticed a common oddity on all users having this problem. They have Hightail (formerly YouSendIt) installed and the icon in the systray was there, but invisible. If I right clicked on the icon and exited...problem solved!

The only thing I can think of is that there must have been an update to the Hightail software that changed something in Office that caused this issue.

Thread can be closed, but I wanted to post in case anyone else has such an issue.