... First of all, please add the PSU info if you request support in other cases. As far as I can tell, this shouldn't be the issue here (unless the issue is way deeper then I suspect), but there are plenty of issues where the PSU is the cause of errors while the computer does 'work'.
On to your issue... Can you start by running the installer in Administrator mode? (If you don't know how - http://www.digitalcitizen.life/how-run-programs-administrator-windows-7 )
If that doesn't help, try redownloading the file and install that one or run AMD Driver Autodetect (AMD Driver Autodetect - in admin if it doesn't detect everything correctly).
If that doesn't work either, it might be a corruption of the Windows Installer. If that is the case, contact Microsoft Support - https://support.microsoft.com/pt-pt/contactus/ - and ask them for help with fixing the Windows Installer (it *might* turn out that you need a complete fresh Windows 7 install, if something went wrong with your previous install)
Win7 and Win8.1 must be fully updated before installing any AMD driver. SP1 and all 'critical', 'recommended', and relevant 'optional' updates must be installed first. Windows Update must tell you 'There are no more updates available'...until you get that message keep installing/rebooting/installing, etc.