iPhone does not charge or detect by pc

So when the phone is off, or the battery is below a certain point, iTunes recognizes it?

Make sure you are entering DFU mode, not recovery mode. Here is how to enter DFU mode:

1. Hold down the power and home buttons for ten seconds, or until the phone shuts off. The phone shutting off is what you want to happen. If its already off, turn it on, or begin the boot process.

2. Once it shuts off, let off the power button and hold the home button until iTunes sees it. If you have to do this longer than 60 seconds, then you failed step 1. If you can't get it, repeat until you are in DFU mode.