Pls help with strange older hardware problem

I ran into a setup with an HP DeskJet 420 hooked to an old, old Compaq
Presario 850 (Pentium I, slow) running Win95. The setup works fine, no
problems.

But when I connect the selfsame printer to a more modern machine, it
insists that something's wrong with the cartridge. (Ink light comes on,
printhead moves to removal position.) I can get it to print a page, but
as soon as I do, ink light comes on and head moves to center.

I've tried it on two different machines with the same results.

I'd like to move the printer off to another machine so we can get rid of
the old Compaq, but this has me stumped. Why would the printer think
itself OK on the old 95 box, but that something's wrong when moved to a
more modern machine? Any hints or pointers greatly appreciated!