The first thing you must be aware of is GM has had a really bad generator design since they changed it starting with the '87 model year. They develop huge voltage spikes that can destroy its internal diodes and voltage regulator, and interfere with computer sensor signals. It is real common to go through four to six replacement generators in the life of the vehicle, however, to reduce that number of repeat failures, replace the battery at the same time unless it is less than about two years old. The battery is the key component in damping and absorbing those harmful voltage spikes, but as they age and the lead flakes off the plates, they lose their ability to do that.
The next thing to look at is if the "Battery" light turns on when you turn on the ignition switch. That light is in the circuit that tells the voltage regulator to wake up and do its thing, which is to run the generator. If that light never turns on, start by checking the terminals in the connector on the side / rear of the generator. That used to be a brown wire.
Next, measure the voltage on the large, bolted-on output wire on the back of the generator. That must always be the same as the battery's voltage. If you find 0.0 volts there with the engine not running, and high voltage, as in 15.0 volts or more with the engine running, there is a break in that wire going back to the battery. There used to be a fuse link wire spliced into that wire, but you are more likely to have a large fuse bolted into the under-hood fuse box.
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Tuesday, September 8th, 2015 AT 8:40 PM