Wait on the Database Engine recovery handle failed. Check the SQL Server error log for potential causes I try installing SQL2008R2 - SQL2012 - sql2014

2014-07-17 16:31:16.00 spid14s     Error: 17190, Severity: 16, State: 1.
2014-07-17 16:31:16.00 spid14s     Initializing the FallBack certificate failed with error code: 1, state: 20, error number: 0.
2014-07-17 16:31:16.00 spid14s     Unable to initialize SSL encryption because a valid certificate could not be found, and it is not possible to create a self-signed certificate.
2014-07-17 16:31:16.00 spid7s      Starting up database 'msdb'.
2014-07-17 16:31:16.01 spid12s     Starting up database 'mssqlsystemresource'.
2014-07-17 16:31:16.01 spid14s     Error: 17182, Severity: 16, State: 1.
2014-07-17 16:31:16.01 spid14s     TDSSNIClient initialization failed with error 0x80092004, status code 0x80. Reason: Unable to initialize SSL support. Cannot find object or property. 
2014-07-17 16:31:16.01 spid14s     Error: 17182, Severity: 16, State: 1.
2014-07-17 16:31:16.01 spid14s     TDSSNIClient initialization failed with error 0x80092004, status code 0x1. Reason: Initialization failed with an infrastructure error. Check for previous errors. Cannot find object or property. 
2014-07-17 16:31:16.01 spid14s     Error: 17826, Severity: 18, State: 3.
2014-07-17 16:31:16.01 spid14s     Could not start the network library because of an internal error in the network library. To determine the cause, review the errors immediately preceding this one in the error log.
2014-07-17 16:31:16.01 spid14s     Error: 17120, Severity: 16, State: 1.
2014-07-17 16:31:16.01 spid14s     SQL Server could not spawn FRunCommunicationsManager thread. Check the SQL Server error log and the Windows event logs for information about possible related problems.
Following can be reason for this error

The account which user selected on Server Configuration page window ( during installation)  is somehow not able to bring SQL Server database engine services online. Either is lacks privilege or it is corrupted. During installation of database engine services SQL Server tries to bring online database services as a internal process but due to startup account either corrupt or not having appropriate privileges it fails to do so and ultimately installation fails.

Other reason is when installation fails first time due to some reason and user uninstall failed installation from add remove program, the un-installation leaves account in broken state so any further attempt to install flashes this error message.   

Solution:

Uninstall SQL Server completely from Add remove program and start new installation by right click on Setup and selecting run as admin. Now when you reach Server Configuration page please select NT Authority\System as SQL Server Database Engine service startup account.



http://social.technet.microsoft.com/wiki/contents/articles/24364.sql-server-troubleshooting-could-not-find-database-engine-startup-handle-error-during-installation.aspx

PS: If this does not helps please revert. Please follow steps mentioned in link carefully