Chosen Solution
The iPhone 5s would not power up after a long period of not being used. At one point, it did display a “charge battery” symbol, but never anything else, even after leaving it plugged in for days. Assumed that a battery change would be sufficient, I replaced the battery, but now it won’t turn on at all. Only clue I have is that a USB power measurement dongle measures .3A/5V when the battery is plugged in (and I believe .08A when disconnected). Also tried a second new battery, with the same result. My goal is merely to power it on long enough to retrieve its data. Full repair unnecessary.
You can send it off to a specialist that can do data recovery. If you haven’t tried cleaning or replacing the charge port that could be the issue. If it doesn’t feel like it’s seating properly, you can take a toothpick or fine tipped tweezers to clean out any dirt and debris from the charge port. If it’s a board level issue, it could be due to a bad charger that has fried the TriStar chip in the phone. If you’re looking for a data recovery specialist, I recommend Jessa from iPad Rehab. She does tons of board repairs and data recovery. Feel free to check out iPad Rehab on youtube as well.