What version and edition of SQL Server are you using? SQL Agent is not available for SQL Express Edition.
If the service account for SQL Agent set up as a login to SQL Server and does it have sysadmin rights?
Have your Windows people implemented any Group Policy Objects that limit access to services? SQL Agent needs to query the status of some services in order to complete its startup.
Original author: SQL Server FineBuild 1-click install and best practice configuration of SQL Server 2017 2016, 2014, 2012, 2008 R2, 2008 and 2005. 1 Dec 2016
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Quote: "When I give food to the poor they call me a saint. When I ask why they are poor they call me a communist." - Archbishop Hélder Câmara