As i can't find a wiring diagram for the car myself this may or may not help but I believe the charge wire out of the Alt goes to the top stud on the starter where it gets connected to the battery cable leading up to the post on the fuse box to join the main lead back to the trunk.
If the ~ 10agw wire is broken or suffered corrosion you may not be charging due to the lack of voltage sensing off the charge wire.
Have you done anything in the starter area lately?
05 Cobalt SS 100% stock.
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