Q: iPhone 5, won't turn on from being charged for hours ?

I have been having issues with my phone keeping  a charge for the last 2 months or so. But today it charged to 100%, within 20 minutes it dropped down to 67% and by the time I got to practice about 15 minutes later it was at 1%. Usually I don't let it stay at 1% for long, I run to charge it, but today I didn't have that ability; it was probably dead for about 4/5 hours, so I knew it would take a while to start back up. I got back to my dorm and charged it with the USB in my MAC, around 1, woke up around 3 and still nothing which was a bit unusual because it did this yesterday and during one of my interviews it turned on 2 hours later. Anyways, I woke up at 6 and still no charge, nothing, I switched the USB to a wall so that it could probably have a more powerful charging source, its going on 7:15 and it has not turned on since this morning; I have tried a hard reset but when the apple is supposed to appear it just goes back black then shows the battery charging again.

Is my phone officially broken ? I would hope not, I don`t have a way to any Apple store and I certainly do not have any $ to be buying another iPhone 5, and coverage? You could forget that.