iPhone 4 cannot be charged via power supply after iOS 7 update
This sounds like a problem with your power supply that just happened to coincide with iOS 7. "Reduce motion" setting will not make a difference. If it's under warranty, take it into the Apple Store and see if you can get it replaced. Otherwise, you may need to buy a new charger.

If you are good with electronics, you can cut open a USB cable, plug it into the charger, and see if the voltages between D+, D-, and Vbus match this pinout.