IPod touch the generation's home button broken and device does not power on

My IPod Touch 5th Generation is 2 and a half years old and it's home button broke about a year and a half ago. I didn't really prioritize fixing it then and instead I just used Assistive Touch but about a year ago my IPod went black and didn't turn on. I tried charging it and nothing helped, so after a week went by with no visible change, I took my IPod to a repair place. When I got there I told them what had happend and the man plugged in my Ipod there and it showed that it had gone dead. My Ipod worked again after it charged and turned back on again. A couple months later the same thing happend and similar things happend up till now but every time, I would just have to wait until it went dead for it to work. But two and a half weeks ago I updated my IPod to IOS 9.2.1 and when it turned off to update it never turned back on. When I press the power on button, the apple symbol appears on the screen as if the IPod is turning on but just goes black a again after around a minute. After a week it showed that it was dead and I was happy, thinking that it would work again but once it was charged it still had the same problem. It also does not appear in my ITunes when I connect the IPod to my laptop so I am unable to run a backup. I have researched my problem and it appears that quite a few others are also in my predicament. Pressing the home button and Lock button at the same time should normally fix issues like that but as said my home button is broken so I am really at a loss at what to do. I just recently got back from vacation and had not backed up the ca. 1500 new photos that I had taken so its an even bigger problem for me, because when you get things repaired, test are run and they could potentially erase the data off my IPod and that is the worst thing that could happen. So if anyone has an answer for me, I would be eternally grateful.