There were so many cheers when Microsoft announced that the .Net 3.5 Framework was no longer a pre-requisite for installing SQL Server starting with SQL Server 2016. Folks were so excited, until they started testing certain pieces of the product, specifically Database Mail. That’s right, if you want to use Database Mail in SQL Server 2016 you have to install the .Net 3.5 Framework.
If you are installing SQL Server 2016 on Windows Server 2012 R2, this might be a problem for two reasons. First, the .Net 3.5 Framework is no longer included by default when spinning up a new install. Second, you will get no errors when testing Database Mail in SQL Server 2016. Mail will be queued, but will not be sent and there will be no errors in the Database Mail log, the SQL Agent log or even the SQL Server error log.
So if you’ve gone through all the usual steps to troubleshoot Database Mail (or these steps) in SQL Server 2016 to no avail, be sure to double check that the .Net 3.5 Framework has been installed. If not, you will need to install it, then apply ALL the patches for it.