My iPhone 5s won’t work after battery died and I plugged in my charger

My iPhone 5s battery died and when I tried charging it the battery icon just showed up for about a second and the phone went off.

whenever I plugged it in after that time it would take about 5 minuets to start and then show a bright black screen then it would turn back off but the body is always warm when I plug in the charger and leave it for sometime . It is visible on iTunes but keeps telling me to update to iOS 12.1 which I did the night before the screen stopped coming up, so I downloaded the update and when it was extracting it showed error 4013,I’ve tried several times but keeps showing. I really don’t know what next to to but I hope it’s not a hardware problem

NB the screen is still black