If your Chevrolet Trailblazer won't start and you suspect a dead battery, check the battery connections for corrosion and tightness. If the connections are good, use a voltmeter to test the battery voltage. A fully charged battery should have a voltage of around 12.6 volts. If the voltage is low, charge the battery and test it again. If the battery won't hold a charge, it may need to be replaced.