HP960c deskjet printer - problem or two

Dollardog

I have an old HP960c printer, I've had newer ones but keep going back to this one because its compact and does what I need it to - or it did!!
For the last few months, its not been printing very well, its been scrunching up the occassional line, only probably a couple of lines on a page. Its not bothered me too much so I didn't bother to fix it, I was told it needed calibrating but couldn't find any mention of it in the HP assistant that came with it and I read somewhere that when I change the print cartridge, it will calibrate itself anyway.
Anyway, its now out of black ink and I put a new print cartridge in it yesterday, but can't get the light to go out that says the black cartridge needs re-seating. I've taken it out a dozen times or more but it won't have it, I've tried taking the colour cartridge out and re-seating that too but although the colour cartridge goes back ok, there's no luck with the black. I put an old, empty cartridge in and that fitted fine and printed but with it being empty, obviously the print was too feint to read. Both the new cartridge and the empty one were the same supermarket branded ones, I mostly use HP ones, but bought those because they were being discontinued, they've worked ok before. I've just sent for some genuine HP ones so I am hoping that those will seat properly.
Any ideas as to why the new cartridge wouldn't seat, shall I just throw it away? Also, will putting in a new cartridge automatically calibrate it or will I have to do anything else?

Thanks in advance for your help.

Dollardog

Well the new ink cartridges arrived today, HP ones. I've tried putting one in but it still has the light warning that the cartridge isn't seated properly.
I really need to get this printer working again, plus I've now got 4 new cartridges for it and don't want to waste them.
Does it need calibrating and if so how can I do that? The colour cartridge is still in and ok. As I said above, when I put an old, empty black cartridge back in it was ok, but won't work now with two new ones.
Help please.

Dollardog

Any ideas anyone?