Chosen Solution

So a friend gave me an iPhone 5 because she could not fix it, it was in recovery mode and the phone looks like it had taken some damage, and before I got out of the recovery mode she had gotten a new phone so she said I could just keep it. There was another problem with the phone that has happened a couple of times to her before, randomly if you tried to turn on the phone it would be like a brick. Nothing. When you plugged it in however it showed a low battery sign, then the apple logo. She says that whenever this happened she would charge it overnight and the next morning it would be fine. I tried that, no success. I have most likely searched the web for fixes and try after try nothing worked. When I tried to restore it from recovery mode or DFU mode iTunes would say waiting for iPhone and then the iPhone reboots back into the loop, usually with the error code 2001. I do not want to take it to the apple store, replace the battery, or do anything that has to do with opening the device. This is only because the phone is out of warranty, not in good enough shape to be worth spending money on, and I got it for free and hopefully it will stay free. It just bugs me because it is just lying around and I would like to jailbreak it, but right now I cannot. My problem is identical to this users post Stuck in continuous apple logo loop, turns off when cable removed? , though none of the fixes helped. I hope someone can help me fix this iPhone 5. And by the way, just because I can, I have it charging in dfu mode right now to see if it makes a difference. Thanks! Update (01/17/2017) Also, I read online that if I heat the phone up it would turn on. Well I tried that and something new happened. It showed the apple logo and then rebooted and then again. So does that mean something, or am I just desperate to get it working? Update (01/17/2017) The previous owner told me the iPhone had never been water damaged, and battery has never been replaced. It looks pretty banged up but otherwise I don’t know why it would not turn on. Update (01/17/2017) Unless there is another suggestion for a fix, I do not feel like it would be worth it to spend money on a free 5 year old device by replacing the battery. But if you have a suggestion that does not involve me replacing the battery please let me know.

boost battery above 3.5 volts Update (01/30/2017) you need a multimeter, do you have one?

it sounds like you just need a new battery its really not hard and doesnt cost much you could do it yourself i got mine stuck in a boot loop it wasnt booting cause it didnt have enough power because my battery was crap changed it and it fixed it other then that you will probably not get anything out of it its dead