Not printing black ink

Have an HP5510 All in one that is not printing with the black ink. The cartridge was recently replaced, the first time, when it was being opened, the cartridge exploded and ink went all over the desk. The second time it was being replaced, the cartridge again exploded, but to a lesser degree.

The cartridge was placed in the printer after being cleaned off, and the printer worked fine for 24 hours. It registered near full ink level. After the initial 24 hours, the printer would no longer print black, and is having difficulty print any other colour.

I have done the recommended procedures regarding care and maintenance, including 'clean printhead', align printer, clear ink smear, print quality report, print status report (both were blank, so that was useless). I have not been able to 'clear inkjet nozzles' because I keep receiving the same message - "printer is busy at the moment".

Any ideas for self repair, or should I simply take it in?