HP DeskJet 812C Hardware Problem! with Printer cartridge carriage. Printer Cartridge retracted into right side of case will not come out. There is No paper jam in machine to prevent it from doing so. Front Panel Top Green Light is Blinking, middle Orange light is blinking, Bottom light is off.

Lift the Flat Bed Scanner up so that you can find the Cartridges Inside.
Remove the Cartridges from the Printer.
Move the Cartridge Carrier Back and Forth as fast as you can!
Replace the Cartridges back to the Printer!
Good Luck!!!!

push down at the top towards the back than pull out

Try using the HP Print Diagnostic Utility in Windows - HP Customer Care (United States - English)

Open the print cartridge door allowing the print carriage to move to the far right side of the unit. Once the print carriage has stopped, lightly press down on a print cartridge to release it. Pull the print cartridge toward you out of its slot

make sure your both the cartridges are working properly and it is not dry just remove the color cartridge and clean it with tissue paper and fix it again . If still there is problem change the color cartridge.
1. Use a clean, dry, soft, lint-free cloth. Locate the copper-colored circuitry strip on the back of the cartridge.
2. Wipe the copper-colored strip with the dry cloth. Use an upward motion, from the nozzle end to the top of the cartridge. Do not wipe the nozzle end of the cartridge or touch the nozzle plate. Wipe the contacts only once.
3. To clean the printer contacts, carefully look for fibers or contamination on the electrical contacts inside the carriage assembly, but do not wipe the printer contacts with any object. The contacts in the printer can be damaged if too much pressure is applied during a wiping process. Try to remove any visible attached debris within the carriage assembly by gently pulling the debris off with your fingers. If the carriage contacts show noticeable damage, contact the Customer Care Center listed in the printer's User's Guide.
Reinsert the cartridge and try printing again. If the error continues, the cartridge may need to be replaced.
Hope this helps. Please rate my response.
Thanks.
Have a good day.

One or both ink cartridge is failed.First remove the cartridges and clean the contacts on the carriage unit using piece of cotton and some alcohol.If problem persist open the cover and look where the carriage unit stops.There is two marks on the left side where the carriage stops.On the carriage there is a yellow arrow.If this arrow show left mark the color cartridge ia failed and need to be replaced.If the arrow show right mark replace the black cartridge.If you replace both cartridges and problem still persist carriage unit or logic board assembly is failed and your printer need service.

unplug the printer and try to move carriage by hand, if it does not move, the carriage mechanism is broken, if it does move, plug the unit back in, if same error occurrs, it is an issue with the printer carriage mech.

Was this a new factory ink cartridge or a refilled one?
I have seen some reconditioned/refilled with the color inks refilled in the
wrong section.

Here write 4 step you do it step by step

1. remove safaty strip from the cartridge
2. clean carridge block contact with soft cloth
3. replace cartridge for short
4. replace carridge block

The printer assumes that the color cartridge is good, and is trying to print with the dead color cartridge.
See if there is a setting for your printer under the control panel, printer, and go to printer properties.
See if you can select to print BLACK only.
I know they have this option for some Canon Printers, but not sure with the HP Printer Drivers.
Worst case senerio, Highlight all of the text, and change the color to BLACK before printing. You can always just pick up a cheap refilled cartridge at Staples since it wont be used a lot, the quality isnt going to make much difference.

Good luck.
Hope this helps.
Mac