After trying a few things (simple stuff like power cycling), and staring intently for a while at the part of the printer that was making the bad noises, I realized what the problem was. There was a printhead plug stuck in one of the moving parts of the printer -- exactly the same orange rubber plug that had been included to protect the ink inlets on the two inkjet cartridges (CM and YK) included in the printer box, sealed in separate packets. I checked my trash, and sure enough, both those plugs were in the basket -- so I'm not the one who dropped the plug in there. This looks like a quality-control problem at the HP assembly plant. Maybe they test the cartridges (most of which are remanufactured these days, not new) right before packing them in the box with the printer, and they dropped a plug when doing that and thought they'd lost it on the floor, but instead they lost it inside my printer...
Since the machine had already tried to start up, and parts had moved around, the plug had gotten pretty badly wedged into the spot where it was sitting, but after a few minutes of effort with long tweezers, I was able to dislodge it; a few more minutes effort and I actually snuck it past the various parts in the way and got it out. And now my printer works. I made a color copy of the cover of Girl Genius (lots of fiddly details to compare). It looks great.
I gave the tech the serial number of the machine. I hope they'll adhere to good Total Quality Management practices and actually send a report to the manager of the relevant assembly and packing plant...