Hello Cory,
Problems seems solved.
I uninstalled HP program and installed it again from the CD, but problem was still there.
So the shop gave me a third reusable ink cartridge (I have been working with this shop for already 2 years with no problem), I did not have great expectations and this time the printer did work, with both a Mac and a PC.
I have been looking through internet and I believe that the problem is that some printers protect the cartridges, so then the cartridges cannot be used in another printer. But I can say that the shop could use the 2 cartridges that would not let my printer work. So if anybody has a better idea of what is happening, would be very welcome.
Thanks you for your help
Maria