Battery death

Changed to the spare battery over the weekend and within about 6 hours the warning light was flashing to say it was flat,  It was bought about 6 years ago 2nd hand so I can't say it owes me anything.  But out of curosity this morning I tested the voltage and it was 12.8volts so I connected a 12v florescent light of about 15w (I think) the voltage went down to 10,44volts and there it has stayed with the light on for the last 8 hours or so with the light still on all the time.  Does this suggest that a cell in the battery has failed?