iPod Touch 5 Won't Turn On

I have an iPod touch 5th generation and it won't turn on. I'm not sure what software update it's running, but I do know that it is a recent one because I have the new emoji's. Anyways it has a storage of 32 gigs and the storage is no where near full. Now a few months ago I dropped the iPod on the sidewalk and it cracked the front screen a little. The crack is on the bottom left close to the home button and a little bit on the screen. Over time the left side of the screen popped up a little bit and sometimes the home button doesn't work. (I don't know if this has anything to do with the problem). A few months after the screen cracked my iPod was dead for about two months straight because I moved and had lost the charger. When I first plugged it in the iPod was very cold and it took awhile to turn on. When it was fully charged and I took it off the charger the battery would last for about 30 minutes or an hour. After awhile the iPod couldn't go 15 minutes without dying but it would turn back on as soon as I plugged it in. Now it has to stay on the charger 24/7 or it will die. I lost everything on it twice. The first time it deleted everything on its own and the second time I had to factory restart it (by holding the home and power button at the same time and then just the home button until it cleared everything) myself because it wouldn't come on at all. About a week ago there was a storm and the power went out, the iPod was off for 24 hours and when I plugged it in it didn't come back on for maybe 3 hours. I didn't do anything to it I just let it sit and eventually I heard the noise it makes when its on and charging. I didn't lose everything on it. When it does go off (like when the power goes out or when the charger breaks or basically whenever its not connected to power) and I plug it back in, it shows the apple logo for 5 seconds then the screen goes black for 4 seconds. It keeps doing this over and over again. If I hit the power button it doesn't change anything. If I hold both the home and power button it doesn't change anything. The most recent time it happened I just let it start up on its own and I just waited. When I factory restarted it I didn't know what I was doing and I was nervous because it was one of the first times it had ever happened. Its doing this again right now and it has been all day. I think my battery might need to be replaced. But for now is there anything I can do to get it back on without losing everything again? I was going to wait two days and if I didn't come back on I was going to factory restart it but I really do not want to. It also hasn't been backed up because if I unplug it for a second to plug it into the computer it dies. I don't know what to do with it this started happening when it was just over a year old and I never used it too much or did anything bad to it. So any advice would be much appreciated even though I pretty much have tried everything there is to try and I guess I'll just have to wait and see. Thanks!