The 1312 installation does a poor job of cleaning itself up after you attempt to remove it. I always go out and manually clean up the crud that gets left behind when I have software related problems like this.
Heres where to go to cleanup everything:
1. Uninstall the software from Programs and Features
2. Reboot
3. Run <install dir>\Util\CCC\Scrubber.exe
4. Run <install dir>\Util\CCC\UPDScrubber.exe
5. Delete C:\Program Files\HP (and any other HP folders)
6. Delete C:\Program Files (x86)\HP (and any other HP folders)
7. Download the latest Full Software Solution from http://support.hp.com
8. Reinstall and try again
The imaging files get cached in the HP directories. The uninstall doesnt always clean up and shut down the scanning services which can block new devices from getting registered. The Scrubbers are additional cleanup tools that purge the registry and other temporary files. Downloading the latest software from the website makes sure you are getting the latest and greatest updates for your model and OS.