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Sony xperia E4 will not turn
but it is charging. it is 90%
and when I unplug the charger
He shows me the red low battery
Repair the phone with XC and check again, if it doesn't work then it's probably a hardware issue that will be have to be inspected by your Local support
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355
That could be a hardware issue.
That's hard to tell, it could be just the battery or it could be something else, it'll be better to get it inspected by your Local support
You might want to call them.