Why won't my phone launch?

For a while my phone has had some problems. I dropped my phone once, shattering the screen, I ended up deciding to replace the screen myself, but this brought on even more problems. The phone wouldn't charge if I had the screen popped into the chassis at the top. I ignored it however and just dealth with it, then one day while I was charging it I accidentally knocked it off my bed (maybe three feet off the ground) and suddenly it wouldn't charge at all. The only way I've been able to use it is if it's been connected to power so I've been using a portable charger. Recently however it's gotten to a point where it will boot to the apple logo then it will go to a backlit black screem and just sits there. I've tried connecting two different batteries to it and that hasn't been the problem it still does it. I can't hold the home and power buttons at the same time either because my home button was broken in repair of the screen. Any help would be greatly appreciated.