Why will the cyllow and Cyan ink cartridges not work?

This sounds like it needs a print head cleaning. It's simple, just touch the "Setup" button (looks like a wrench and a cog) and then touch "Tools", then "Clean Printhead". It may need more than one cleaning done, which does use up ink, but is necessary sometimes to clear the lines. I've had this happen many many times. Are you using HP replacement inks or generic refills? I had a printer completely die on my from using generic inks, it can really damage some printheads. If you need more of a step-by-step solution, you can search your browser for your printer name (HP Officejet Pro 8600) and I am sure something from HP's site will turn up in the results for your to reference. Good Luck!