After upgrade to 2016, can't view SQL Server Logs
Windows patching and majid's solution is what worked for us too. Just adding my 2c that may help others. We have a cluster with 2008, 2014 SP2 and 2016 CU2. After upgrading an instance to 2016, we had the following errors:


2014 and 2016: syspolicy_purge_history job failed on step 3
2016: SQL agent would start then stop
2016: Couldn't view SQL error logs


Windows patching, which primarily applied .net security patches fixed the syspolicy_purge_history job in 2014. The new ODBC driver fixed remaining issues in 2016.

Note: installing 2016 SP1 before installing this driver (https://www.microsoft.com/en-us/download/details.aspx?id=53339), will install a newer ODBC driver, that appears to have the same issues when running on a cluster. We attempted this on a test environment, but had to uninstall SP1 and the new ODBC 13.1 driver, then install CU2 and the other ODBC 13.1 driver. Haven't attempted to install SP1 again yet