I just bought a Lexmark Z738 - it prints black OK.
(Windows XP - driver from the CD in the box)
Try printing out a test page. This should bypass all the software settings in the previous answer.
Do you see any black text on the test page?
If not then there may be a problem with the print nozzles or the cartridge.
The 738 uses all 3 colors blue red and yellow together to produce a near black colour.
It may be that
a) there is no red and yellow ink in the cartridge
You can check this when you print a test page - a dialog pops up which should show the levels of all 3 ink colours
b) the cartridge is not properly aligned with the nozzles
Check that the catridge is properly mounted in the holder.
c) some of the nozzles on the cartridge are still blocked by protective tape
Take out the cartidge and check that no residue is left from the protective tape. Try wiping the cartridge nozzles with a tissue to clean them