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My Sony Xperia Z1 has no Frame anymore, but I don't thonk it changes too much. It started having this problem when it still had a frame. When I connected it to a wall plug it didn't charge but stayed at 1% - it didn't change over 2 days and it didn't show it charges. Today it went dead but even when I put it on a wall plug nothing is changing except the light is flashing. When I press vol up and power for 3 seconds, it vibrates 3 times, then flashes red three times. Then it goes completely black again. What can I do ? All my data is on this phone and I bought it only a year ago! 
What do you mean by "frame"
Connect your phone to a wall charger > press and hold power & volume up for 10 seconds > let it charge for 2 to 3 hours
If that doesn't work then contact your local Xperia Care
I tried it and charged all night. It still is not turning on but now the red light flashes. I do not have warranty on this phone anymore, how much would it cost to actually let someone look at it ?