Hi Failquail
my first guess by what you explain would rather point towards an issue with the battery itself - since you describe it powered off again after short time and at least after a few attempts.
What´s pointing from your point of view towards internal storage?
We had that question in a german section of this forum where @Incanus gave the feedback that mainboards (Edit: Mainboard for FP3) never were sold stand alone.
(source: 🇩🇪 Fairphone 3 lädt nicht auf - #11 by Incanus )
Unless you´re fully sure it´s because of the internal storage I´d recommend to reach out to a Fairphone Angel if this is possible for you.
Best
DonFnord