iPhone5s Corrupted Firmware? (Boot Issue)

Hello everyone,

Here is the issue with my iPhone 5s. Recently I forget to charge it. and I assume it died because The screen was off. Now here is the weird thing. I unplugged the phone and it turned off completely. Once i plug it back in the Apple logo come up (for like 1- 1.5seconds0 and then it's just blank slightly lit (back-light) I let it charge and the apple logo came up like normal and stuff. I tried placing it in DFU mode but it wont? I tried placing it in recovery mode but it wont? There was no iTunes logo appearing, and the phone wont go to Complete black-screen after doing the DFU Mode steps. Now i just took the phone to replace the battery But i still got the same results with a brand new battery. The techy guy suggested it was the Power IC. But how can that be if the phone can charge and turn on? These are what all that doesn't come up after apple logo goes out:

1. No Charge icon

2. No iTunes icon.

The only thing that happens after the apple logo goes out is a slightly backlit screen that is constant (unplugged and plugged in) Sometimes the phone doesnt turn on at all when it is not plugged in.

NB//

When i plugged it in to my pc, iTunes detected it in recovery (i recovered and install the new firmware). But now still the same Results. "Apple logo comes up for 1-1.5 seconds, then a blank backlit screen, with No iTunes logo or Battery Logo appearing" Any suggestions other than a Power IC? (which i highly doubt is the problem.) I want to add one final thing. I did drop it, But I had it in an OtterBox case, additionally. I took the phone out of the case and thoroughly inspected the phone and found no outside or onscreen issue.