After battery replacement my screen flashes to the apple logo then off

I replaced my battery about 4 months ago and everything was fine until the past week. My phone started to turn off randomly and very often so i figured it was my battery being loose because i could hear it shake when i moved it. So i used double tape and taped my battery down where it isn't touching anything. After that my phone worked for a day and then it started to turn off again randomly and sometimes would just go to the apple logo then off and sometimes when I shook my phone it would work and when it was plugged in it would work. And finally starting today my phone wouldn't turn on when it was plugged in, so i took my phone apart and put everything back together and now when i tried to turn it on it flashes to the apple logo then goes to a dark grey. When I try to connect it to my apple computer it doesn't even recognize it.

Bottom line is, is it my battery that is bad or my hardware.

Thanks!