Errors around 96% usually mean that the installation cannot find the printer objects that it wants in your printers and faxes folder. In my experience that is a result of a Universal Print Driver hijacking your installation and renaming your printer objects before the installer has a chance to get to them.
Run the Uninstaller and then take a look at the scrubbers that HP provides. The scrubbers can be found in your installation files under <root>\util\ccc. There is a Scrubber.exe as well as a UPDScrub.exe. Run these two guys at a minimum. You can also try running the Uninstall_Lx.bat jobs to clean up any excessive rubbish left behind from previous failed attempts.
After the scrubbers have done thier job then make sure the UPDs and any additional HP drivers have been removed from the computer. We dont want anything interfering with your next attempt.
Rerun the install and you should be able to get through everything without issues.