'colour cartridge is not compatible'

You need to reset the chip in the cartridge that tells the printer when it's low. The part can be found on sites that sell refill kits.

1. Go to menu set as default.
2. Do color calibration.
3. Print PQ test pages, observe the colors, chk
4. Print demo page. chk
5. Print from different file/system..

HP 21 black and HP 22 tricolor cartridges are the cartridges compatible with HP DESKJET D1560.HP 27 and 28 won't work with your printer because they won't get recognized by the machine.It will only give you an error message like incompatible cartridges.

Is a cartridge toner problem, only happens with some alternative toner cartridges
Try with another cartridge.(Q5942A or Q5942X)

The error states that you are using non-HP cartridges for all colours. If black prints fine then you should replace the colour cartridges with genuine HP colour carts. You should be able to get a refund on the refills since they clearly do not work as intended.

I think that spring must have gotten loose that holds the cartridge in place, right hand side, put it back where it belongs, might want to compare with the other, black cartridge side.  Good Luck!

I had the same problem and solution was change the cartridge for a new one (My printer is a HP PSC 1315)

ITS NOT THE BLACK CARTRIDGE!!! Try changing the colour cartridge and see what happens. When a 9600 checks ink levels it does the black ink first, then the colour, if the colour is low it goes back and checks the black again but will constantly give an error message for the black cartridge. Sounds bizarre but try just the black cartridge in with no colour. print a test page in black only, if that does not print then it is a fault. Also make sure the driver is updated!!!

replace the colour cartridge aLSO AS IT NEEDS some specific colour to start this allignment and to complete but the colour is not getting printed so this error.
remove the cartridges from the printer.unplug the printer for some time.then again ON it and insert the cartridges and try .
sometimes it helps.

I had the same trouble with a rebuilt cart from Staples, try HP brand or Nukote brand. Nukote cost less and work great for me!