iPhone 3GS stuck at logo and reboots

[zumdude]

I was given an iPhone 3GS and when I first got it, it had no battery life left. I kept it charging on my pc. When it finally got to the apple logo, it just stays there. Every few minutes or so it will reboot but will still stay on that logo and it's hard to tell if it's charging or not. iTunes isn't showing that it is. I have tried recovery mode DFU mode, even jailbrake and all with same results. Only difference is with jailbrake that I was able to see it charging, but that's it. nothing else. I'm not sure if it's a software or even a hardware issue.