Why won't my phone turn on?

First, let me start off by saying thank you for taking the time to help me out. On to my question now.

I have a iphone 5s that at about a year ago would turn on and had a mildly busted screen. I deployed and came back home to it not turning on. So I took it to the local repair shop to just get the screen fixed and after the installation of the screen, it still wouldn’t turn on. So I charged it for a full day to see if I could get a charge on it, no luck. So me not wanting to put much more money into like taking it to a repair shop, decided to buy a battery off Amazon with the tools to repair myself. The replacement went well, I connected all the pieces properly (watched all the iFixit videos), so I charged it again for an hour. NO AVAIL. So I left it on the charger for a day and night. No Avail again. So I get on here and many other forums to look for possible solutions to my problem. Heres the list:

1) Hold the battery button for 3 seconds, let go. Immediately hold the power button and home button together for 10 seconds, then let go of the power button and just hold the home button for 5 seconds. Rinse and Repeat as often as needed, off and on the charger connected to the computer.

2) Just hold down the power button till something happened, didn’t work.

3) Hold the power button and home button together for 20 seconds (I did this and for a minute) connected to the computer and not.

4) Replace the lightning adapter since the phone wasn’t recognized by my MAC. Still not working.

Im lost as what to do next. Beside replace the power button. But I don’t think that is it because it would charge and turn on before I left it sitting up without being charged. So if anyone has any opinions that don’t concern the DFU, Restart, and of the like methods that I mentioned, please let me know. I have put a lot of hours into this thing now, and thats why I want to fix it now. Yes I know its an old phone and outdated but I have a purpose for it, a 3 year old kid for car rides.

Thank you again,

Jonathan