Issue is already fixed but thought it may help someone if I posted the method.
I had Outlook open on my Taskbar while playing a game. The game crashed to where I had to re-start with Outlook still open. On a re-start Outlook refused to open. It would open the splash screen but just sit there forever 'processing'.
The fix was actually quite easy. I opened my Control Panel then Programs and Features. From there I right clicked on Office and selected to 'change'. I had two options; Quick Repair and On-line Repair. I tried the Quick Repair first but it did not resolve the issue. I then tried the On-line Repair and all is fine including my PST file still being intact.
The difference between the two repair methods appears to be that the Quick Repair will only replace files that are detected as being corrupted. The On-line Repair pretty much re-installs Office 365/2016 to the point that you have to confirm your account but it does not mess with with the active PST file or email account log-on. In other words after the repair everything was exactly as it was before the issue.