2 x HP Envy printers (Shoreham-by-Sea BN43)

I have 2 HP Envy printers
1 x 5540 & 1 x 5541
Both work, but they are not reconizing my black ink cartridges
There could be an issue with the cartridges, but i am wary of buying another and wasting my money
My work has now bought me a new printer, due Thursday
I have a new colour ink cartridge and the two black cartriges (open) the printer will not reconize ( one is way out of date)
As well as 2 x power leads and 1 x USB cable

If anyone can take these and make them work, i would be really happy, rather than them being thrown away.

Fair Chance Policy: I’ll wait before choosing a recipient to give more people a chance to reply.