Battery sign on dead Droid Turbo, won't turn on?

[AC Question]

I've had my Turbo for a little less than a year. Overall, I've been more than disappointed with mine, but that's something beside the point. Maybe. Keep in mind throughout this question that the charging port in my phone was broken, and when I charge my phone, I have to lean the cord in a certain direction for it to say it's charging.

The battery on my Turbo sucks (just saying), it has since after the week I got it. It normally only lasts maybe 5 hours. But it functions, and normally I can get through the day. Except for the last few days. In the last few days, I've gotten it up to a max battery of 30%. It's not that it won't charge up, I got impatient and unplugged it, it's that it's charging VERY slow. Like maybe 5-10% an hour.

Today it died around 5%. Ok, fine. I plug it in. It's been plugged in for 5 hours, and it still only shows the battery sign upon pressing the power button. I've moved it around the house with me, but it's been on the charger for roughly that time. I've had a green LCD light up, and the battery sign. At one point it had 3%, so I turned it on, but I had so many notifications it drained the battery back to 0%, turning it off.

Does anyone know what I can do to fix this?