Replacing the battery would be a good first step to try and solve the problem. Also, the reason you’re having issues with DFU mode is because by the sounds of things you’re not in DFU mode in the first place. To enter DFU mode follow these steps:
# Plug your phone into your computer with iTunes open
# Press and release the Volume Up button
# Press and release the Volume Down button
# Press and hold the Sleep/Wake button until your phone’s screen goes black
# Press and hold both the Volume Down and the Sleep/Wake button for 5 seconds
# Release the Sleep/Wake button while continuing to hold down the Volume Down button
# After about 5 seconds iTunes should detect an iPhone in recovery mode
You can be sure you’re in DFU mode if iTunes detects your phone in recovery mode and your phone screen is black. If your phone shows anything other than a black screen, try following the steps again.
Hope this helps!