I suggest that you buy a replacement cartridge. If I remember correctly this is
a monochrome printer so only one cartridge needs to be replaced.
From the symptoms you describe the cartridge may have failed electronically in
which case no amount of attention will repair it. The cartridge used in this
printer is non-foam filled so if you shake it you will hear the ink sloshing
about unless it is empty.
If you really do want to try cleaning it, wash the printhead under a drizzling
cold water tap (just the printhead itself not the whole cartridge), gently
press the head down onto some kitchen towel lying on a bunch of newspaper (to
protect the bench). If there is any ink coming through it will show on the
towel, you should get a well defined rectangle of really black ink, if not
repeat several times. If this does not work then only special equipment will
fix it (not worth it for such a low cost cartridge). Some people have reported
good results after soaking the head in warm water, or steaming it from the
kettle, do this with extreme care.
Just some comments, it is extremely unwise to try to clean the printhead as you
described unless you know exactly what you are doing. Printheads can be
seriously damaged with the oils from your fingers, with minute particles from
cleaning material etc. Wiping the head itself is very likely to damage it, just
dry it after washing as described above on the towel. I don't think cleaning
will fix this cartridge but you could try.
Note: The above procedure should not be attempted with any cartridge other than
the type used in certain HP printers with cartridges that have printheads built
in; using this procedure on Canon, Epson or any other printer components is
more likely to result in you buying a new printer than anything else...
Tony