iPhone 5 dead after battery ended

I have an iphone 5, it was working fine for couple of months. I used a non-apple charger and battery started drain fast and after battery ended iphone not powering up. I used other battery and phone started working but when the second battery ended phone not powering up again. Seems that charger can't start the phone if battery is completely empty, if battery is not empty phone charging with no problem but the battery drains very fast, it is dead in 4-5 hours even if the phone is in sleep mode.Is this issue u2 ic? Can someone confirm that i need to change u2 ic? Thank you for your help!