It sounds like it's the Cyan cartridge causing the problems, you said if you push on the cart it will recognize. In this case you can apply 1-3 layers of masking tape to the top of the cartridge, where it snaps into the printer itself. You will see where there is an indent just behind the control chip, this is how it's held into place in the printer, apply the tape 1 layer at a time until you get a good fit.
You will find when 1 cartridge gives an error, that others will do the same, normally 3 that are side by side to the culprit cartridge. You may also have the same fit issue with the M cartridge as well, you won't know until you solve the Cyan fit problem.
Let me know your results, Kindly-Kelly