My battery connector on my iPhone 4 will not charge my battery.

You would really need to be more specific about the problem in order to get a great answer. Here are some helpful tips though.

Have you tried using a different cord? A different brick? On the iPhone 4 a lot of dirt likes to accumulate in the charging port. If you have something like a paper clip you can usually clean it out. Be careful though, you could easily hit the pins.

If you have tried all of the above you may need a new charging port or possibly a battery. Unfortunately without more information I couldn't be more specific on what to do next. Best of luck!