If the phone does not boot with a known good battery, it is likely a motherboard issue. If you’re experienced with microsoldering it may be worth the effort, otherwise I would invest in a new phone or send it off to a professional! Also, just to be sure, I would disconnect the power button cable and try booting it up. Sometimes a faulty cable will cause boot issues.
Hey Alex! If it worked prior to repair, it is either a loose connection, or it was damaged during disassembly. I would disassemble, inspect connector for any debris, and ensure it is properly connected. If so, it may need replacement.
Hello! I have to mention, if you installed it yourself, it is likely not an apple battery :( unless it was pulled from another phone used. Try a new battery, to see if it is just defective. What was the problem initially?
Hey Chris ! Yes it is the Home button Flex. you can find it on ebay if you'd like to replace it https://www.ebay.com/itm/New-Home-Button-Flex-Cable-Replacement-part-for-iPad-Air-1-1st-gen/381013464148?hash=item58b62c1454:g:Z...-Rxs:sc:USPSFirstClass!89123!US!-1
No, apple does not sell replacement batteries, so anybody saying they are original batteries is lying. There are high quality aftermarket or used original batteries available however. I recommend going straight to apple and taking advantage of their battery replacement program. I believe its only $29
All this does points to either a faulty battery or board issue. Hopefully just the battery, but these boards are failing at an alarming rate for the iphone 5s due to it's age. Especially after a drop. I would have a shop plug in a new battery just to test. Should be free to diagnose if they're one of the honest ones, or a small fee from the major brands. If that doesn't help, you likely have a cracked solder ball caused from the drop that's making the phone act up.
Sounds like either a bad battery, or damage from the disassembly. Hopefully just a bad battery! Quickest way to test is to install the old battery and see how it responds. If it boots up fine, bad battery, if it reacts the same, it is either the new faulty battery or board damage.