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Uninstall all sql instance, remove any temp folders, restart the system.
Install SQL Server in administrator role/login, restart, then run the exe as "Run as Adminsistrator" role. Might helps you...
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I assume that the log is an event log and it is teh security events that are the problem. Do you understand that? The event logs are where Windows puts various error messages and information messages. Originally there were System, Security and Applicaiton logs but now there are many more. So it appears that there is something that SQL Server wants to tell you about security and it cannot. Are you sure that the correct account is being used for SQL Server?