iPhone 4s keeps boot looping

My apologies for the very long post. I recently got myself an iPhone 4s for cheap. However, it keeps repeatedly showing the apple logo for a few seconds, and then it turns off. It does this repeatedly not matter how long I charge it. It doesn't even hold a charge so when I unplug it, it'll instantly turn off and won't turn on until it's charging again, even after I left it on charge for hours. At first I thought it was the battery so I bought an ifixit battery, but it still boot loops even after replacing the battery and cleaning the contacts with isopropyl alcohol. Luckily I had an old beaten up iPhone 4s at hand which still turned on and charged but the screen wasn't doing too great. I tried the ifixit it battery inside the old beaten up 4s and it charged and held the battery fine. Even the original battery of the boot looping 4s worked fine in my older beaten up 4s. Does anyone know what I can do from here or is this a lost cause? Any advice would be appreciated.