Summary.txt listed below:

Configuration file:            C:\Program Files\Microsoft SQL Server\100\Setup Bootstrap\Log\20150626_152929 ConfigurationFile.ini

Detailed results:
  Feature:                       Integration Services
  Status:                        Failed: see logs for details
  MSI status:                    Failed: see details below
  MSI error code:                0x1603
  MSI log file location:         C:\Program Files\Microsoft SQL Server\100\Setup Bootstrap\Log\20150626_152929trin_aide_Cpu32_1.log
  MSI error description:        
  Configuration status:          Passed

  Feature:                       Management Tools - Complete
  Status:                        Failed: see logs for details
  MSI status:                    Failed: see details below
  MSI error code:                0x1603
  MSI log file location:         C:\Program Files\Microsoft SQL Server\100\Setup Bootstrap\Log\20150626_152929\trin_aide_Cpu32_1.log
  MSI error description:        
  Configuration status:          Passed

  Feature:                       Management Tools - Basic
  Status:                        Failed: see logs for details
  MSI status:                    Failed: see details below
  MSI error code:                0x1603
  MSI log file location:         C:\Program Files\Microsoft SQL Server\100\Setup Bootstrap\Log\20150626_152929\trin_aide_Cpu32_1.log
  MSI error description:        
  Configuration status:          Passed

  Feature:                       Business Intelligence Development Studio
  Status:                        Failed: see logs for details
  MSI status:                    Failed: see details below
  MSI error code:                0x1603
  MSI log file location:         C:\Program Files\Microsoft SQL Server\100\Setup Bootstrap\Log\20150626_152929\trin_aide_Cpu32_1.log
  MSI error description:        
  Configuration status:          Passed

Could you please zip and keep C:\Program Files\Microsoft SQL Server\100\Setup Bootstrap\Log\20150626_152929 folder on OneDrive and share a link in reply.

I can have a look at log and give you some pointers.

Please share the log details, Meanwhile check this link also:

http://blogs.msdn.com/b/sqlserverfaq/archive/2011/06/06/problems-may-occur-when-you-try-to-install-sql-server-2008-r2-shared-features-if-the-temp-folder-is-encrypted.aspx

If its due to MSI/MSP Files missing, follow the procedure :

https://support.microsoft.com/en-us/kb/969052

Cause

• The folder that you are trying to install the Windows Installer package to is encrypted.
• The drive that contains the folder that you are trying to install the Windows Installer package to is accessed as a substitute drive.
• The SYSTEM account does not have Full Control permissions on the folder that you are trying to install the Windows Installer package to. You notice the error message because the Windows Installer service uses the SYSTEM account to install software.

Refer this link for resolution

https://support.microsoft.com/en-us/kb/834484?wa=wsignin1.0