Could not find database engine startup handle error means SQL Server installation was able to install SQL Server services but when installation is trying to start SQL Server services its failing.
A simple solution I mentioned In This Technet Article is
Please go to SQL Server configuration manager and locate the SQL Server services
Right click on SQL Server express service and select properties and change startup account to Local System and select apply then OK. This will start services with Local system account privilege.
Certain reasons which can cause 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.
The reason can be also that SQL Server installation was successful in installing SQL Server and its services but due to some other limitation in system or other system related errors SQL Server is not able to come online.
In Your case reason is
2015-02-08 19:55:06.16 spid14s Error: 17190, Severity: 16, State: 1.
2015-02-08 19:55:06.16 spid14s Initializing the FallBack certificate failed with error code: 1, state: 20, error number: 0.
2015-02-08 19:55:06.16 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.
2015-02-08 19:55:06.16 spid14s Error: 17182, Severity: 16, State: 1.
To solve this Either start SQL Server service account with Local System or Create a new local account having admin privileges on the local machine and try starting SQL Server service with that account. This Blogs.msdn article says such error can come if account profile is corrupt
As you are already aware running SQL Server service with account having admin privileges is not advised. In such case for time being you can run the account with local system but you can use Configure Windows Service Account and Permissions to create account with minimum privileges.
EDIT:
FCB::Open failed: Could not open file
E:\sql12_main_t.obj.x86Release\sql\mkmastr\databases\mkmastr.proj\MSDBData.mdf for file number 1. OS error: 2(The system cannot find the file
specified.).
2015-02-09 10:42:45.12 spid8s Error: 5120, Severity: 16, State:
101.
2015-02-09 10:42:45.12 spid8s Unable to open the physical file
"E:\sql12_main_t.obj.x86Release\sql\mkmastr\databases\mkmastr.proj\MSDBData.mdf".
Operating system error 2: "2(The system cannot find the file
specified.)".
2015-02-09 10:42:45.12 spid8s Error: 17207, Severity: 16, State:
1.
As per below logs SQL Server is searching for msdb file at location
E:\sql12_main_t.obj.x86Release\sql\mkmastr\databases\mkmastr.proj\
Can you manually move both msdb data file and log file to above location. I know this is not your desired location but let first SQL Server come online then we can use alter database command and change location to what ever suits you. To me this is bug and is happening because SQL Server is unable to ,somehow, decide the location of msd files and so choosing random location.
Revert if this does not works
Best Answer
What OS are you using?
To get a fresh installation you have to remove the data directory, after removing the mssql-server package:
And then:
This will delete all your user databases, but will also remove the system databases, which will allow you to reinstall and, hence, re-specify the SA password upon reinstall.
Let me know if this works.