IPhone 3GS won't turn on unless plugged in?

I dropped it a few days ago and at first, it would turn off as soon as I unplugged it, I took it to a local repair shop and it looked to be done, they changed the battery and now it'll stay on for about 15 mins of usage after unplugging, it cuts off and when you turn it back on it shows the apple logo for about a minute and then cut off again, same happens when I do the old sleep+home thing:/

Also I'm not sure if it's worth mentioning but when it's not plugged in, the battery percentage stays constant for about 10 mins, but when I reboot it, the battery percentage is much lower than it was when it died

Any help would be appreciated

Take it back.