iphone 5c won't turn on. When plugged in, it's showing the low battery sign and apple logo but that's all.

Sunday (2 days ago), I was taking a nap. Before I took my nap, the phone was turned on. When I woke up, I checked my phone and it wouldn't turn on. I assumed it was dead. I went to charge it, and the low battery sign popped up. Then seconds later, the apple logo sign came on the screen so I thought it was going to cut on. Waited a few seconds, it went right back to the low battery sign. It keeps flashing back and forth from the apple logo and the low battery symbol when it's plugged in. When it's not plugged in, it doesn't even do anything. Tried charging it for hours, still the same thing. Tried seeing if it was my charger, nope, charged perfectly on other iphone 5s. There's two options I think could be wrong: my new lcd screen which is a little cracked already and also damaged. OR my battery, which was working perfectly before I switched to the new lcd screen. PLS HELP!!!