I have seen something similar before when the account the SQL Server is set to run under does not have the required permission.
Tangentially, once it is installed, a common mistake is to change the login credentials from Windows Services, not from SQL Server Configuration Manager. Although they look the same, the SQL Server tool grants access to some registry keys that the Windows tool does not, which can cause a problem on service startup.
You can run Sysinternals RegMon/Sysinternals ProcessMon while the install is running, filtering by sqlsevr.exe and Failure messages to see if the account credentials are a problem.
Hope this helps