See its not that much a problem with the carriage moving(cartridges moving back and forth in the carriage station).
It's basically the rollers at the front of the printer which are attached to a rod.
Now when you give a print command the hardware card of the printer recognises the command and that rod which holds the rollers comes down and then the paper is picked now this may not be a resolution however this is what you can try.
With the printer On pull out the power cable from the back of the printer and then the walljack.
Wait for 30 seconds or more so that your printer is resetted to a basic factory state and then plug in the cable to the wall and then to the printer once it powers on try to print if it still doesn't then you have a hardware problem on your hand and the printer is old.
Also follow this document and see if this helps :
http://h10025.www1.hp.com/ewfrf/wc/document?docname=c00035263&tmp_task=solveCategory&lc=en&dlc=en&cc=us&product=304431
But call in to hp at 1800-474-6836 and ask them for the upgrade options which you will get at a 50-60% discount or above depending on the printer and you will get an Carepack that will save your printer from falling into a hardware problem for $1 (80-90% discount).
I know this isn't exactly a resolution but if you feel that I have atleast replied to your post I would appreciate any amount of thumbs up ,if you think it's really helpful then please reward me with a 4 thumbs up.
Thanks!