I have seem quite a few clogged print heads that were clogged in one or two colors. They can be unclogged still. You need to soak the print head with Windex. It takes a while. You will ned patience.
But, in this case, we know that magenta and cyan ink can flow through the print head because it came out on the Windex-soaked paper towel, and yet it will not show up on the nozzle check. So this is not a clogged print head and cannot be fixed with a Windex soaking. It's an electrical problem that cannot be fixed except by replacing the print head.
UV light test for OBA'a on a variety papers