The above statement is *entirely* false. The DeskJet 940 (as well as
all DeskJet printers) do not block printing for an empty cartridge.
Period.
For the OP's problem I would try the following: first try printing a
self test page as shown at:
http://h10025.www1.hp.com/ewfrf/wc/document?lc=en&cc=us&docname=bpd07098&dlc=en&lang=en#N1272.
If the test page prints OK then check the cabling and connections to the
printer. If the self test does not print please note any blinking
lights or other errors. In this case, open the printer lid with the
power turned on. There are some icons molded into the top part of the
printer case and the carriage will move to one of these positions, which
indicate either no error or a problem with the black or color cartridge
or the black or color cartridge being low on ink. [As noted before, the
cartridge being low on ink will *not* prevent it printing.] See
http://h10025.www1.hp.com/ewfrf/wc/genericDocument?lc=en&cc=us&dlc=en&docname=bpd09173#N285
for details.
If the indication is that one of the cartridges has an issue try
cleaning the contacts as shown at:
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=bpa02060.
Regards,
Bob Headrick, MS MVP Printing/Imaging
The low on ink indicator is designed to let you know that the ink is
getting low and you should have a replacement cartridge available. You
can continue to print until the cartridge actually runs empty, or the
print quality deteriorates.