As I Understand your HP Deskjet F4480 recently started making a very loud & rapid clicking noise when printing,
Don't worry as I'll be glad to help, however, to provide an accurate resolution, I need a few more details:
Does it print fine while using a copier? (Printer standalone)
Did you check if the carriage is moving freely? (Manually when moved by hand)
While you respond to that, here's a few things you need to know:
Remove the color cartridges and check if it prints fine with the black cartridge only.
Also about the Clicking/grinding sound, If it's heard when the printer is turned on or when it is printing. Blinking lights may accompany the noise. The problem can be caused by a carriage stall or a paper jam.
Turn the printer on.
For the 800, 900, 3820, 5500, and 6000 series, open the top cover of the printer. Verify that the carriage moves to the center of the printer. If the carriage does not move to the center, proceed to step 2.
For the 5100, 5600, and 5800 series printers, open the top cover of the printer. Verify that the service station (the piece below the cartridges) lowers, allowing access to the cartridges. If the service station does not lower, proceed to step 2.
Unplug the power cable from the back of the printer.
If the carriage moved to the center, or if the service station lowered, remove the cartridges. Check inside the printer for any broken parts.
If the carriage did not move to the center, try to manually slide the carriage to the center. If the carriage is locked either in the left or right position, proceed to step 5.