Can a faulty print cartridge be the cause of blue and green printing issues?

Absolutely. A defective or faulty print cartridge, even a new one, can cause printing problems, including only printing certain colors. Try swapping the blue and green cartridges to see if the issue follows the cartridge. If the problem moves with the cartridge, the cartridge is likely faulty and needs to be replaced. Contact HP support or the cartridge manufacturer for warranty assistance.