A message keeps appearing 'cartridges not in correctly' or similar, I have taken them our and replaced them on a number of times and this hasn't helped.

Hi this is only a try for you not know if it will work but better than nothig.

Some HP machines have 3 reset levels.

I do not know if the 5610 had them but it's worth a try.

Power off printer, then press and hold buttons while powering on, if it doesnn't reset, then unplug it and press and hold buttons while plugging it in, please tell us if the machine even tries to reset.

# and 3 Partial Reset

# and 6 Semi-Full Reset

# and 9 Full Reset

A Full Reset will clear any stored information in the printer, speed dials, etc, so always start with a partial reset and work your way up.

Please come back and just gave a vote, it will gave me some satisfaction to know am helping some one so I will keep on helping.
All The Best: Pineworks