My phone won't turn on? Xperia E3

I brought my Sony Xperia E3 in 2014 but I had no issues with it until this year. Earlier in May/June my phone wouldn't get rid of the login screen (those waves sort of thing) and my phone went really hot but the phone was fully charged. Anyway I managed to fix that problem by letting the battery drain and then re-charging it and turning it on using the power button and the volume button.

Now my phone won't turn on again. Yesterday night I switched my phone off and slept (battery was at 81%), but when I woke up this morning my phone wouldn't turn on. When I press the power button it shows me the 'Sony Xperia' page when you first switch it on but then the screen goes black after a second. I tried charging it but when I plug it in the red light flashes for a second and the 'Sony Xperia' screen appears and then goes black again and it keeps repeating this. I tried rebooting my phone following steps online but it won't work (when pressing the power button and volume button it vibrates for 3 seconds but has no response but a black screen, I tried this a few times). What should I do?