Photosmart C4580 "damaged or missing cartridge"

Hello tara38840,
Try this manipulation to see, no guarantee, but it sometimes helps!
Keep the printer running and unplug the USB cable from the back of it.
Remove the cartridges.
A message should appear after a while asking you to reinstall the cartridges, do nothing.
Printer still running, unplug the power cord from the back of the printer and wait for one to two minutes.
Reconnect the power connection, if the printer won't start, turn it on using the power button.
Replace the cartridges, it may require a calibration or print test, proceed.
Reconnect the USB cable, restart the computer and try printing.
See you later
--
The one who does not bring pleasure upon arrival ALWAYS brings pleasure upon leaving!
Breton Proverb

In fact, no, because I don't have any in advance, and frankly, it would annoy me to buy some if the printer is dead ;-) Plus, they're not old.

I found some cartridges, so after changing them it works, but I hope it won't happen to me too often.

In any case, thank you for your advice;-)