You can run a hardware self test page on the HP Deskjet 5550 printer, which does not involve your computer at all.  If the test page prints, you know that the printer is still in working order.

Turn the printer off, and remove the USB cable from the back.  This ensures that the printer is not connected to the printer.  Now turn the printer back on.

Once the printer is ready, press and hold the power button.
Press the Cancel button eight times, then press the Resume button four times.
Release the power button, and a test page should print.