Well, let’s list as many possible causes of a seemingly dead phone that we can think of, and then try and substantiate or eliminate them with this specific case. But it’s a good idea to contact official Fairphone support quickly, as already suggested by AnotherElk.
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Water damage.
Has your phone been in the rain, on the beach, did it fall into water, or otherwise get wet, at any time in the last three months since you’ve had it? See waterwiki and point 5. -
Can you think of any other event that might have a bearing, either physical or regarding software? A drop or other shock? An update that didn’t conclude properly? Charging with the wrong voltage? Did the phone get very hot at some stage?
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Battery failure (unlikely but I suppose worth checking, especially if the phone has frequently been getting very hot).
Leave the phone off, plug in a cord to charge. Does anything happen?
Try and find some means of getting the battery’s voltage measured. Any electronics technician or enthusiast could check that for you.
Perform a spin test: place the battery flat on a perfectly clean, flat surface. Try to get it to spin around. If it shows the slightest propensity to carry on turning when your fingers release it, then it’s damaged and must be responsibly disposed of and replaced. It is dangerous in this state. -
Poor battery connection.
Ensure that the battery is properly seated in its compartment and cannot move.
Inspect the terminals and the contacts of the compartment for visual signs of damage. -
Poor contact between modules.
Disassemble the phone, (see here for help) removing all the components. Check all contacts for damage and clean using a cotton bud soaked in isopropanol or surgical grade alcohol (90° available from chemists/pharmacies). -
Failure of a major component
This can be checked by replacing modules one by one, with spares. Ideally, try to find out if there’s a Fairphone angel in your area (see here for details), and / or someone who has the same model and could spend some time with you testing replacement modules one by one.
I think it would be wise to enlist the help of a Fairphone angel in any case, if there’s one near you.