HI DrTony2013,
I'm sorry to hear that you are experiencing issues scanning with your Photosmart 7515 since upgrading to Mavericks.
You indicated that you downloaded and installed the full feature driver for your printer and Mavericks. I've checked and the full feature driver for your printer is different from the one you gave; you gave HP-Inkjet-SW-OSX-Mavericks_v12.34.44.dmg and HP's website shows the driver download as HP-Inkjet-SW-OSX-Mavericks_v12.34.38.dmg. I've included the link to the correct Mavericks download.
Please install the proper driver to see if that corrects the scanning issue.
HP Photosmart 7510 e-All-in-One printer series - C311 Full Feature Software and Drivers - OS X 10.9 Mavericks