My 3600dn indicated need new cyan cartridge. I installed new one

That message is saying you need to replace the blue "Cyan" ink cartridge in the printer. When the printer detects that the ink in out it tells you to replace the empty one to continue printing. Just buy a new cartridge install it and you will be good to go.

1. New original ink tank will dried for several times of head cleaning procedure.

. ....ran a nozzle check and cleaned print heads because it wasn't printing any ink on the paper.... ???
Nothing at all? If yes, problem is in the printer main board. Lost electricity to the head.

The Cyan print head nozzle maybe blocked.
If deep cleaning does not fix it then you need a new print head.
The cost of a new print head is expensive and it maybe better to get a new printer.

Run the PQ Troubleshooting diagnostic
Check out the BLACK page.
You can also run the Disable Cartridge Check diag.
This test will enable you to pull all the cartridges out, and put the black into any other slot. Then print the Configuration Page and see if the problem follows the black cartridge. If it prints good this way. Put the Cyan into the top slot(black), print the config page. If it prints bad, it's not the cartridge it's the printer.
I think that replacing the Black Cartridge should solve your problem.

You don't state what type of printer, but many require entering the maintenance menu section to indicate the cartridge is changed. Consult the printer's manual (you didn't throw it out, now did you??)

The dot could be from the cyan toner cartridge. There could be a mark or scratch on the image drum surface underneath the cartridge shutter. If it is a toner mark it can be carfully cleaned with a lens cloth. If scratched or nicked the cartridge will have to be replaced.

It might a problem of mismatch cartridge. The printer is not detecting the cartridge as is it not getting the exact type of the cartridge, check the exact cartridge number and type and install it.

The problem seems from your new cyan cartridge.
It doesnt print cyan ink.
Try to clean print head and test print for each color
from the utility menu

ensure that the one you install is the exact model name and number, if this is correct, try unistallling once again and check one more time,

you might want to get a new cyan toner if this still fails, i dont think there is a prob in your machine, cheers

Hi , The 59.61 is a problem with the Cyan print cartridge drive motor and occurs during startup or rotation. The first thing you will have to do is replace the cyan drive motor and if that doesn't correct the problem then the dc controller. But I'm pretty sure the motor has failed for the cyan. Now I'm not talking about replacing the Cyan Toner Cartridge!!!!