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Press Windows and R keys and this will bring Run. Then type control printers and press enter. Do you see your printer there ?
We can install latest drivers for you printer and that should add the printer back with correct driver. Go to this website --> http://support.hp.com/us-en/drivers/selfservice/HP-Officejet-J4000-All-in-One-Printer-series/3645081/model/3645099
Download the "HP Officejet Full Feature Software and Driver" and make sue to select Download Only and this will download the latest printer software. Then open the downloaded file and install it. While installing, it will allow you to install the printer, so do it.
Please let me know if that didn't work, so we can continue troubleshooting