MS SQL Server installation fails with error message
There is an entire directory of logging done by the installer. If you are getting this from the graphical popup try looking in the \Setup Bootstrap folder under your installation of Sql Server. This is created whether it succeeds or not. The path is something like so...

C:\Program Files\Microsoft SQL Server\110\Setup Bootstrap\Log

In there you will find logs in separate folders by date and time. Like so..

\20160502_124028

Start with the Detail.txt log going all the way to the bottom and work your way up looking for anything with the word 'error' in it. That should give you more information about what is happening.

Also, I do see an access violation in the middle of your stack. That is:
HResult : 0x80004005

Hi Sofia,
     The detail.txt is a good place to start. It does refer to the file that was inaccessable. It is: "C:\Program Files\Microsoft SQL Server\MSSQL11.SQLEXPRESS12\MSSQL\Binn\perf-MSSQL$SQLEXPRESS12sqlctr.ini" at the very beginning of the stack.

Whether or not this is the issue with the other editions of Sql Server you attempted to install I couldn't say. However if you aren't logged in as local Administrator while trying the install you should log in with the local Administrator account and retry the install.