Any knowledgeable electronics repair shop should be able to pretty quickly determine the source of the issue by observing if the phone draws any current with an ammeter, dry-fitting a new charging port and new battery, and observing the response through the ammeter.
A bad tristar might still result in the phone drawing current, but won't allow the battery to charge. To be certain, a known working battery might be dry-fit onto the phone and if the phone still won't charge the new battery, then a tristar repair is indicated.
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