Why won't my phone turn on? Working on iTunes

Hello. Thank you all in advance for trying to help. Let’s get to the point.

iPhone 5s won’t turn on. Two nights ago I left it to update to the latest system while on a charger. The next morning, the phone died.

I tried a hard reset as described and nothing. I tried to search for a possible backlight problem with the flashlight but I couldn’t see the logo.

While connected to my computer, iPhone appeared in iTunes after a hard reset asking for a recovery. I did this 2,3 times, then iTunes could recognize it immediately and show all the information(battery info as well) but the phone won’t turn on. I never tried to repaired a phone so I wanted to check with you all.

I bought this phone from a guy who replaced the broken screen 3 years ago.