Thank you. As mentioned in my post it is the Windows Installer version. I will follow your instructions and let you know what I find.
Any luck? Did you figure out exactly what it was that was causing 3.3.8 to keep opening? Was it the icon pointing at the wrong executable? 
Thank you. Never did figure out what was wrong. It finally upgraded. After upgrading the wallet (Windows Installer) to 4.0.9 from electrum.org, using the link in the wallet, I received the following error message when attempting to send funds. I have never encountered this message before.
The server returned an error when broadcasting the transaction.
Consider trying to connect to a different server, or updating Electrum.
Unknown error