Chosen Solution
I have this iPhone 4, that I remember dropping. There’s a problem after dropping it. The screen start to flicker before it starting to fade away. I try to turn on the phone and soft reset it, but it won’t turn on unless I plug it into the cable. Even when it’s turn on, It will be stuck froze at apple logo for hours. I would like to identify the problem and repair it.
This sounds like a battery issue. Apple devices act goofy even when they are plugged in if there is a problem with a bad battery. Could also be a problem with the screen causing the device to not boot up. Ether way, the battery should probably be replaced as it’s more than a few years old now if it’s the original. Might be a better option to get a new phone based on how much it will cost to fix it. Especially if you need a new screen and battery.
Most likely your battery or battery connections.
Try other cable or probably your battery is the problem.
take a toothpick and clean the fuzz out of your charge port. That might fix it. Seriously. Junk can get in there.