Can't use Nexus 5 if it's not plugged in charger

[gtrani]

Hello all!

I have a Nexus 5 since December/2014 and since last March it started to turn off ramdomly when in use. If I try to turn it on it turns off again during the boot.
I have to plug it in to a charger (wall or USB) to use it, even if it's with full battery.
Additionally, the battery manager seems to have a problem, once it shows that there's no app consuming battery and the predicted time of 3h to discharge almost full battery (please find the screens attached).

Does anyone know what's happening or is facing the same problem?
I tried "googling" this problem, but seems I'm the only one! :'(

Thanks in advance!

 

[N4Newbie]

Try starting the phone in Safe Mode and see if the problem persists. If it goes away, you may have an app installed which is the cause. Otherwise, you have a hardware problem or a corrupt OS.

Turn the phone on then press and hold the power button for several seconds until the "Power Off" banner appears. Now, tap and hold the Power Off banner until "Restart in Safe Mode" button appears.

 

[gtrani]

Thank you N4Newbie!

I just started the phone in safe mode and the problem persisted.

I noticed also that the phone is charging too fast (charging in wall or in USB). I tested once letting it discharge completely and then I charged it fully. It charged from 0% to 100% in about 1h.

Before this problem starts, when using Google Chrome, a page saying I had a virus on the phone was showed and my phone started to vibrate. Then I had to press "home" to stop vibrating and try to use the Chrome again. It occurred frequently and then stopped, but this problem of turning off started.

Maybe a virus on the phone is causing this problem?
I tried AVG and PSafe to scan any virus on the phone, but nothing was found.