Issue in installing SSIS MS-SQL2012
The problem is apparently not related to just SQL 2012; it has been reported on older versions also.

One guess is that your copy of SQL Server is probably corrupt. You could try downloading from a different source and checking if the issue repeats. The new SQL Server download might have all the required files in good condition, and save you the headache of any issues down the line. Of course, you should uninstall everything before attempting a fresh install from a different source.

You mentioned that it was Enterprise Edition? Assuming that it's a licensed copy,  you can also call Microsoft Support and ask them for assistance.