oh, just another thing - is it possible for a print head to be damaged,
so that it only prints in magenta?

Printheads are glorified lightbulbs. Well they are more complex than a
lightbulb but are prone to burnout just like a lightbulb. While
cleaning should be part of troubleshooting, keep in mind that the
lifespan of a given head is officaly somewhere between the 10th and
20th cartridge change on current generation printers. I don't have the
specs on the bjc-4200 though I presume you are using the thumble sized
bci-21 and bci-21C so that number could be 20 to 30 changes. If you've
printed that much... or more, head burnout is likely.