iPhone 4 Won't Charge at All

Inspect the charging port area for dirt/debris/fluff build-up that may be preventing a good connection and use a wooden toothpick, soft clean toothbrush, or a can of compressed air to clean it. Also look for bent or broken pins. Try another cable and/or charger block (be sure to always use a genuine Apple certified brand) in a known good outlet. If you're using a USB port, try another port. If you're using a hub, try a direct connection. If you're using a USB port in the front of a desktop computer, try one in the back. If all these fail, make an appointment at your nearest Genius Bar to have the device evaluated.

I had a similar problem where the screen was blank and didn't appear to be charging, and wouldn't turn on.

Somewhere I found a suggestion to reset the phone, by holding the power button (top of iPhone on right hand side) and and home button (circle button at middle bottom of iPhone until the Apple symbol shows. (In my case it's white Apple logo)

Made me very happy, phone works and don't need to buy a new battery. Just yet.

Hope this works for you.

My Iphone 4 is now not charging at all since I took it to the Apple Store and they 'wiped' and reset the operating system 😟