I agree with the dead battery speculation, there's a good chance that's the issue as you said it was "left in the closet for quite awhile" and again you mentioned it was hardly used. Boot loop would be a typical symptom of a dead battery and can happen easily when left drained for some time. Wonder why somebody would want to replace a logic board without trying the most obvious and cheapest solution first. C'mon Apple, you can do better than that, can’t you really hire and pay decent techs ?
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Try a battery replacement, if you want to do it yourself here’s the relevant guide:https://www.ifixit.com/Guide/iPhone+SE+Battery+Replacement/61303
I agree with the dead battery speculation, there's a good chance that's the issue as you said it was "left in the closet for quite awhile" and again you mentioned it was hardly used. Boot loop would be a typical symptom of a dead battery and can happen easily when left drained for some time. Wonder why somebody would want to replace a logic board without trying the most obvious and cheapest solution first. C'mon Apple, you can do better than that, can’t you really hire and pay decent techs ?