Time to pull out the ol digital multimeter. Let the car sit over night and without trying to start it and without putting the key on- check the voltage on the battery. If it is over 12.56 volts the battery is good. Take some black silicone and seal the crack in the top of the battery. Clean the negative terminal one last time. What I do to my terminals when I clean them is to coat them in vasoline - works great forever to prevent corrosion. Cheap and almost everyone has some. If the battery reads UNDER 12.56 volts after resting overnight - say 12.25 volts - it is weak and should be changed. If it reads 11.50 volts - or there abouts - you have a shorted cell and the battery is toast. After you have determined the battery is good, start the car. The voltage at the battery terminals should now be 13.32 volts- 13.89 volts at idle. At fast idle the voltage should climb to 13.67- 14.47 ( somewhere in that range depending on your alternator output). If your voltages are lower - change the regulator and brush pak on the alternator. My voltage tests may sound complicated - but is real simple and tells you exactly where you stand with your charging system.