Last year, I had a TF400069 error when installing Team Foundation Server 2013. This year, while installing Team Foundation Server 2015 for a customer, the error reappeared.
Did I learned nothing?
In this case, the situation was a little bit different than before. I no longer installed the Reporting Services component on the TFS application tier. As a consequence, the SQL Client Tools Connectivity libraries were missing on the application tier. These libraries are required to let TFS talk successfully to the data warehouse.
To solve it, load the SQL Server installation media on your application tier(!), start the installation wizard and enable the Client Tools Connectivity.