It seems like you got all your bases covered with this most recent report. You have cleaned up everything that I would normalyl do to get an installer up and running.
All I can conclude at this point is that your Win8 installation has corrupted whatever it needs to complete the installer from HP. Win8 doesnt seem to be able to recover and the corruption is beyond the control of the installer itself. In my opinion it would be a better use of your time to ditch this printer model or to reload your Win8 OS from scratch.
If you have quick access to a different pritner model you could try to install him as a confirmation on the corruption. If the PC can load other printers then you can conclude its an installer issue for that printer alone. If two different printer models have the same problem then its the OS that has been corrupted and needs to get reformatted/reloaded.