I'm thinking you need to start with the battery.
Charge the battery fully with a separate charger. Let it rest 2 hours, then measure the voltage across the terminals directly with a meter. What is it? It should be at least 12.6v for a lead acid, uptimes to 13.2v for a lithium.
If the battery checks out, then it's time to test the Reg/Rec and Stator. But start with the battery because any tests performed with a suspect battery are unreliable.