C310a installer incorrectly believes the driver is already installed (Win7-64)

For the last two weeks, I have been trying unsuccessfully to install my HP C310a on my HPE-150t 64-bit Windows 7 desktop.  I downloaded PS_AIO_07_C310_FSW_Full_Win_enu_140_246.exe and ran it innumerable times, trying wireless and USB connections.

I have tried: disk cleanups; %temp% folder deletes; system restores; L3 uninstalls; computer, router, and printer hot and cold boots; inf folder deletions beginning from my first installation attempt; "Add a Device - Photosmart Prem C310 series" desktop shortcuts; firewall disables; non-Microsoft service disables; start-up program disables; anti-virus disables; and every imaginable combination of all of these.  And probably a few others that I'd be embarrassed to report.

The USB installation never finds the printer, but Windows installs everything but the printer driver.  Wireless installs get to this window    and exit after an interminable pause.  The installation apparently times out while at 50%, and then goes to 100% with a big red "X".  I have hot and cold booted the printer during the 50% stretch with no effect.

HP Print and Scan Doctor finds the printer and reports that it isn't installed.  It recommends that I download and run the latest version of the full install package.

I finally broke out of the do-loop and started reading log files.

The latest entries in hpzinstall.log all report "Result=3221227110:ERROR_SUCCESS_ALREADY_INSTALLED".  Evidently the installer believes that its work is done, but the printer is not listed in "Devices and Printers".  HP Print and Scan Doctor finds the printer and still reports that it isn't installed and continues to recommend that I download and run the latest version of the full install package.

I'm not falling for that one again.

I haven't contacted HP support because HP says my printer is out of warranty, although I took the printer out of the sealed box two weeks ago.  That's a different long story, and I'm too hard-headed to pay for what I believe should be free regardless.

I believe that the installer finds a particular file or registry entry that leads it to erroneously conclude that the printer has been installed.  Therefore, if I could delete or amend the installer's signpost, then it would see the error of its ways and do what needs doing.

Any suggestions?