How do I bypass the wrong cartridges, install original print cartridges that were shipped with you printer error?

if you update drivers or used windows 8, HP make drivers check if cartridges are original, you have limit used of the printer, if you install original cartridges resolve you problem.

A critical firmware error has occurred.

1. Turn the printer off and then on.
2. Try printing a job from a different program. If the job prints, try printing a different file from the original program. If the message appears only with a certain program or print job, contact the software vendor for assistance.
3. If the message persists with different programs and print jobs, disconnect all of the printer cables that connect to the network or the computer.
4. Turn the printer off.
5. Remove all memory DIMMs or thirdparty DIMMs from the printer. (Do not remove the firmware DIMM in the lower slot J1).
6. Remove the printer EIO card.
7. Turn the printer on.
8. If the error does not persist, install each DIMM and EIO device one at a time. Turn the printer off and then on again after installing each device.
9. Replace DIMMs and EIO devices as necessary.
10. Reconnect all of the printer cables.
11. If the error persists, replace the firmware DIMM.
12. Replace the formatter and calibrate the printer.

Ideally it is important to replace with the original type as the specifications may vary and result in poor performance giving such errors.
Before you try to do any repairs replace with the original after un-installing the set cartridges, maybe un-install and reinstall drivers once again.

What is a incompatible print cartridge? The printer "Thinks" that the print cartridge, is NOT an original HP PhotoSmart one. Even print cartridge have chips.

Make sure you removed all the shipping tape from the bottom of the cartridges and that you installed the cartridges in the correct bays.

That happens when the print head sensor does not detect the cartridge.

To start unplug printer power cord for two minutes, and see if this can reset the error.

The wrong cartridge error may be caused also by a bad cartridge, therefore ,as first step you need to est a different cartridge, possibly a new original one.

Check also if the cartridge metal sensor inside the ink carriage is dirty and must be clean, in this case use isopropyl alcohol and cotton to clean metal contacts inside the carriage.

If that cannot fix the problem, then there is a lose connection on the wires connected to the ink carriage / print head assembly. TWhen that happens, the wires connected at the back of the ink carriage must be tested and eventually replaced.

Printer display says: Print cartridge problem : [Tri-Color]. Refer to device documentation to troubleshoot. I can find nothing in the 'device documentation' to help me.

IssueAn 0xc18xxxxx or 0xc19xxxxx ink system error code displays on the front panel. The printer cannot copy, receive faxes, or print. Solution
Press the On button to turn the printer off. 
Unplug the power cord from the back of the printer.
Remove all the ink cartridges.
Wait two minutes.
Plug the power cord into the back of the printer.
Press the On button to turn the printer on. 
Install the ink cartridges when prompted.
If the error code does not display, the issue is resolved.
If the 0xc18xxxxx or 0xc19xxxxx ink system error code displays on the front panel, service the printer.

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HP Color LaserJet 2600n Printer - Installing Print Cartridges When a print cartridge approaches the end of useful life, the control panel displays a message recommending that to order a replacement. The printer can continue to print using the current print cartridge until the control panel displays a message instructing to replace the cartridge. The printer uses four colors and has a different print cartridge for each color: black (K), cyan (C), magenta (M), and yellow (Y). Replace a print cartridge when the printer control panel displays one of the following messages: Replace yellow cartridge, Replace magenta cartridge, Replace cyan cartridge, Replace black cartridge. The control panel display also indicates the color that should be replaced (unless a genuine HP cartridge is not currently installed). Change the print cartridge

1. Turn off the printer.
2. Open the front door. CAUTION: Do not place anything on the transfer belt (ETB), which is located on the inside of the front door.
3. Remove the used print cartridge from the printer.
4. Remove the new print cartridge from the bag. Place the used print cartridge in the bag for recycling.
5. Grasp both sides of the print cartridge by the blue handles and distribute the toner by gently rocking the print cartridge from front to back. CAUTION: Do not touch the shutter or the surface of the roller.
6. Remove the orange shipping locks and the orange shipping tape from the new print cartridge. Discard the shipping tape and shipping locks according to local regulations.
7. Align the print cartridge with the tracks inside the printer, and using the handles, insert the print cartridge until it is firmly seated.
8. Firmly close the front door.
9. Turn on the printer. After a short time, the control panel should display Ready.
   NOTE: If a cartridge is in the wrong slot or is the wrong type for the printer, the control panel will display one of the following messages: Incorrect yellow, Incorrect magenta, Incorrect cyan, Incorrect black.
10. Installation is complete. Place the used print cartridge in the box in which the new cartridge arrived. See the enclosed recycling guide for recycling instructions.
11. If a non-HP print cartridge is in the printer, check the printer control panel for further instructions.
    NOTE: When replacing or changing a black print cartridge, a cleaning page will automatically print. This helps prevent speckles on the front or back of printed documents. A cleaning page can also be generated using the control panel or the HP Toolbox.

Try holding the "resume" button (triangle in circle) for about 10 seconds for each cartridge.
If that doesn't work, go to a refill shop and ask if they have a re-setter for your cartridges. Most shops do.
The re-setter gives new serial numbers to the cartridges, so the printer thinks you have put in new ones. Or you can buy one.
In 99%, when the printer tells you that one of the cartridges is empty, it's actually not. The chip is the one that tells the printer when to stop printing. If you bypass the chip, you can continue printing.
Hope that helps!