Help Phone stuck on "Android starting up, Starting apps"

[dottenator]

I ran my phone's battery out yesterday, and each time I plugged it in to charge it barely got any juice before shutting off. When I did get it to turn on, it booted normally. I left it charging overnight, which succeeded and filled the battery, but it is now refusing to actually turn on. When I attempt to boot it up, it gets past the normal LG screen and goes to a black screen with the words "Android starting up" and, in smaller font, "Starting apps". There is a loading circle, but it runs indefinitely with no visible change. The phone will not respond to anything unless the battery is forcibly removed, and every time I force it off by doing so and start it up again it returns to the same screen. I am reluctant to do anything which would lose data on the phone, as it has not been backed up recently, but I also don't know how to get it to boot at all so I can get at any of the data.
I am running the latest version of Lollipop, as far as I know, and my phone model is LG-H345.