Yeah, sounds like the battery cells are dead. If the battery is fairly new or it worked with no hesitation the day before, then your alternator may have gone. Also, if the alternators voltage regulator went out, then it may have applied too much voltage to the battery, killing it.
Once you have your battery checked or replaced. Get a standard digital multi meter from walmart or the like, costs like 10 bucks (very useful to have), and put the red lead on the positive battery terminal, and the black lead on the negative terminal. Start the car, you should be reading around 14 volts DC. This is the charge voltage to the battery from the alternator. If its too low, the battery won't charge, too high and it will effectively kill the battery.