My phone isn't turning on but it's charging?

First, my lock button is broken.

So, my phone has been dead for 8 hours and it's been charging ever since. I've even unplugged it a few times to give it a break but it's typically charged for an hour and a half at one time before unplugging it. When I plug it in it comes up with the empty battery symbol on the front, so it is charging and responding, and when I unplug it, it shows me the connect to power symbol. I can't hold the power button and the home button at the same time because my lock button doesn't work so can I have some advise on what I could do please?!:)