OK so I have a really good feeling HP wouldn't put a corrupt file on the internet, so this could be related to your registry. First, uninstall everything related to your HP Printer by going to add/remove programs in your Control Panel. Reboot PC.
Download CCleaner, run a backup first, then clean out the registry, reboot PC. Next I like to run Disk Cleanup (Start button>>All Programs>>Accessories) and reboot again. Computer will be clean of corrupt files now.
Next, make sure your printer is on your wireless network using the Wireless Setup Wizard from the front panel of the printer and remove the USB cord. Lastly, try HP Printer Install Wizard again and tell me how it goes.
Good luck!