Was that a new battery? If not, your new generator may have failed. Repeat failures can be reduced by installing a new battery when the generator is replaced unless the old battery is less than about two years old.
Measure the voltage right at the generator's output terminal when the problem occurs. If it is substantially higher than the battery voltage, look for a break in that wire from the output terminal to the battery. On newer vehicles it goes to a large bolted-in fuse in the under-hood fuse box. Those nuts often work loose.
Also monitor the voltage on the small brown wire plugged in near the back of the generator. With the ignition switch on, that should be real low before you start the engine, and the "battery" light on the dash should be on. Once the engine is running, that voltage will be close to 12 volts which turns the dash light off.
If the drive belt is not loose and slipping, and the voltages don't show an obvious problem, suspect a failing voltage regulator inside the generator.
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Tuesday, March 5th, 2013 AT 3:56 AM