The 710c probably works in epp/ecp-parallel mode on the pc (this is an enhanced version of the good old parallel printerport standard). Try to find out if you can disable this mode on the printer (maybe the manual 'll tell you how, probably not) if can set the printer to normal (also called bi-directional mode) the printer will work on the falcon. Try to use an old printer cable, maybe the printer then selects the right mode automaticaly. Maybe you can ask your HP reseller. good luck.
RE: HP Deskjet 710c and ATARI?