When I Plug It In to Charge It Restarts In A Loop

Hi. When the iPhone 5 is not in DFU mode, when I plug it in the USB, it restarts in a loop to the Apple logo. When it's in DFU mode which I believe is also called restore mode (by pressing Home Button then plugging it in until it shows the connect to iTunes graphic or when I hold both Power and Home button for 10 second then hold the Home button for 7 seconds which also shows the connect to iTunes graphic).

I can't restore it using the latest iTunes iOS because as soon as it gets to the waiting for iPhone part, the iPhone seems to restart or turn off and iTunes would report that it cannot restore it that there's an unknown problem.

I may probably need to order a new battery from iFixit but I'd like to try jailbreaking it. What jailbreak app could probably restore this better than iTunes?

I wish I could downgrade it to lower than iOS 8.2 but it seems only iOS 8.2 is signed (the rest is unsigned at this time).

Other suggestions are welcome.

God bless, Rev. 21:4