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Try putting it on the charger, without turning it On.
Or, does it turn On automatically whenever you connect it to the charger?
Has the phone been dropped onto a hard surface (floor without carpet, street, for instance) at any time in its three years? has the phone gotten distinctly damp, or wet outright, at any time in that three years?
I'm glad it has been well-taken-care-of.
So when you put it on the charger, it turns itself On, then Off, then On, etc.?
That's severe 'misbehavior' by a device. It really shouldn't do anything like that.
It will need its battery replaced, at very least. It isn't under warranty after 3 years, I don't think (correct me if you know I'm wrong. The usual warranty period is one year.)
Would you like to take it to a shop local to you?
Or replace the battery yourself (in case it might fix it - not quite 100 % certain at this point) ?
Or would sending it off for repair be preferable to you?
That's a good question.
If you go with Motorola Global's repair services, you have a wait time or turnaround time of four days at very minimum, if you are willing to go with Advance Exchange (more or less like, once they confirm you have started to send it to them, they ship you a replacement, and you never see your original device again... and you must pay the Fed Ex fee for overnight or fast delivery... but, you get a replacement quickest this way.)
Or longer than four days, of course. Standard Exchange is about five or six days turnaround time.
which claims to have a 48 hour turnaround time on mail-in repairs, but that's 'domestic service'... from France, and back to France, might be quite a bit longer, if they even do that sort of servicing.
And, there's https://www.phonerepaircompare.com/motorola-smartphone-repair-services/broken-motorola-droid-maxx-screen-glass-diagnostic-repair-service.html
which quotes a price for battery-type repairs, of about $85. But that's the repair price, and shipping it to them will cost more.
The other two services, Motorola themselves and the second choice also, only give estimates of price by arrangement - in other words, no up-front price quote (since services and problems differ, etc.)
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