C410 Printer Not responding to Mac

[LobsterChop]

My dad has a Mac Mini running Mavericks, and has a Photosmart Premium Fax all-in-one printer that has worked fine for years.  Recently I noticed his router wasn't password-protected, and since we couldn't find the original password, i reset the router with a new password (router is Linksys E1000).  His computer connects wirelessly fine, as does their television, so the router is working. But the printer wasn't found.  I finally got everything right and reinstalled the printer. Ok: Mac says printer is connected and it's in the printer list with a green light and listed as Idle. 

Printer's wireless test report says PASS on everything in the diagnostics summary.  Signal quality is Excellent.  Network name is correct.  Test report says "No problems found. Congratulations on the successful setup of your wireless printer."

But when I try to print, I get "The printer is not responding."  I had updated the softwre for the router when I reset it, but didn't think it would be much of an issue, and still don't know if that's part of the problem since the router appears to be working and the computer and printer both say they're connected just fine. 

I tried to download any updated drivers from the HP support page, but the site says it can't locate any drivers for this operating system for some reason I can't figure out.  It identifies the system as MacOS Mavericks and then says it can't locate any drivers for that system.

I've tried everything I can think of to fix it, including many hours searching for answers online and have come up empty.  I've restarted the printer, restarted the computer, unplugged the printer, uninstalled and reinstalled the printer.  I haven't yet reset the printing system since I worry that'll screw up his laser printer that is still working, although that one is connected by wire.

The only discrepancy I can find is that the HP Network configuration page lists the last #s of the IP address as .100 and the computer's network page lists it as .140.  But again, all tests and reports show the printer IS connected with Excellent signal quality, so I don't know if that's an issue or not.

Since I reset the router, I also can't get my mother's Olde Windows laptop to find the router, which may or may not be connected to this printer issue, although I assume not.  I should note that I'm not a computer expert, although I muddle along pretty well and can usually figure these little things out.  But these have me stumped.  Any advice?