Printing Errors or Lights & Stuck Print Jobs

My black and color HP ink Cartridges were showing low on ink and to replace them.  I took them out and replaced them with a black in cartridge  (65) that I purchased last week and a color Ink cartridge (65) that i purchased months ago.  After I did that the printer read "cartridge problems, remove and reinstall".  It showed they were both empty when in fact the cartridges were not.  I had ink on my fingers from them.  I put the old black cartridge with the new color one and printer still would not work and then I tried the old color cartridge with the new black one and printer still would not work.  It is hard to believe that we got to Original HP ink cartridges at different times that are both defective.  The new color cartridge I bought months ago was in a pack of 2 (one of black & one of color).  I didn't need the color at that time.  So, I used the black ink cartridge from that pack and it worked fine.  We were printing fine until we ran low on ink.  Any suggestions would be appreciated before I try to return the cartridges.

Thank you.