wait on database engine handle recovery failed
It sounds like you have TLS 1.2 enabled, but:


you're not running a build of SQL Server 2012 that supports TLS 1.2, and / or
you're not running a version of the .NET Framework that supports TLS 1.2


The following KB lists out the 2012 builds that support TLS 1.2:

TLS 1.2 support for Microsoft SQL Server
- SP2 
  - 11.0.5644.2 (CU 10) or
  - 11.0.5352.0 (GDR update)
- SP3
  - 11.0.6518.0 (CU 3)
  - 11.0.6216.27 (GDR update)

The .NET Framework version you need depends on your Windows Server version, and is listed out in the following KB article:

FIX: Error when you install SQL Server 2012 or SQL Server 2014 on a server that has TLS 1.2 enabled

It's also possible that you don't have TLS enabled at all, which is required to run the product.  So the solution may be that you just need to enabled TLS 1.0 or SSL 3.0 (although 1.2 is recommended).