Diagnosing electrical problems requires a step by step logistical approach. There really isn't enough information in your post to guide me to help you to find a specifically failed part. However, in a car of that age, it would not be unusual to have badly corroded battery and alternator cables. Over time, the heavy copper wire can break down, even under the insulation where you can't see the problem. Also, the ground connections can corrode, especially the connection where the negative battery cable is bolted to the chassis and engine. I'd like to think that the shop that replaced your alternator is sharp enough to find your problem.

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