Recently Microsoft has released an update (June 2016) for its Microsoft Office 2013 products. The update caused the Mail Applet in the control panel to stop working. At the moment, Microsoft is still looking for the solution for this, and has released a temporary solution, which is to revert back to previous version and prevent from updating it to the newest version.
Please find the process as below :
Open command prompt, as administrator.
If you are using a 32bit OS, use this command :
cd %programfiles%\Microsoft Office 15\ClientX86
If you are using 64bit OS, use this command :
cd %programfiles%\Microsoft Office 15\ClientX64
Then type this :
officec2rclient.exe /update user updatetoversion=15.0.4823.1004
A box will appear and do a repair.
Once it is completed, open your Outlook. Click File, then Account. Look for Update Options, and click Disable Updates.
This will prevent you from updating the software to the latest version.
Tried on my machine and it works!