HP Print and Scan Doctor can't connect to HP Officejet Pro 8600 Plus.

Question

My HP Officejet Pro 8600 has been working perfectly for the last 1+ years, up until 2 days ago, when it stopped printing jobs submitted from my Windows 7 desktop.  I've tried all manner of repair, thus far unsuccessfully, including
resetting the IP on both the printer and the desktop
trying wireless connection, no difference
reinstalling drivers and firmware
hard-resetting the printer
repeatedly trying to print test pages
repeatedly restarted the Print Spooler, and rebooted the desktop
attempting to troubleshoot using HP Print and Scan Doctor.
Additional facts:
My wife can use the printer from her work laptop without any problems.
I can ping the printer from the desktop at its static IP, so IP-level connectivity isn't the problem.
The standard print queue view indicates "(Offline)" in the title bar, and attempting to print a test page from the Properties dialog submits the page, then Status flips to "Error - Offline - Printing", despite the fact that the Properties dialog shows no checkmark next to Use Printer Offline menu entry.
The Doctor finds the printer at its IP and acknowledges that it's installed, and when asked to Fix Printing, says that everything checks-out okay with the product.  However, when I ask it to Test Print, it comes back with a pop-up stating it's Unable to Communicate with Printer; it suggests "Click Help for additional assistance information.", but there's no Help button.
If you've experienced this printer in a similar firmly-wedged state, I'd deeply appreciate hearing how you fixed it.
Thanks,
-Richard (Personal information)

Answer 1

Hi @Sunshyn2005
I timed-out waiting for advice, and contacted HP Support, who helped me get the printer back on the air.  While we didn't manage to root-cause it, in the course of trying various things, the tech disabled Norton 360's firewall, which then allowed connecting to the printer, and restoring print service, which remains up after re-enabling the firewall. 
The timing of the disconnection doesn't neatly corellate with any Windows updates.  My own theory is that it was caused by a 360 update, but am unable to find a smoking gun, since 360 doesn't provide update history.  The exact root-cause remains a mystery, but at least provides another thing for folks to try should they find themselves in similar straits.
I really appreciated your hint that a Windows update might be the root cause, and your pointing out how to review the history and back-out updates: this morning, I found that Windows had installed a batch of updates overnight, and found that no browsers worked.  Using your advice, I rolled back the update, restoring browsing.
Thanks,
-rjs