My iPhone 4 (model AI332) won't turn on or charge
The real answer is you can:

a) pay someone to test a new battery in the device and tell you if it's just the battery
b) buy a new battery (or one that is so old and used, that it doesn't hold a long charge, but works well enough to restore the device when it's being powered from a computer).

There's no way the internet can do the diagnosis on one device with the details you have provided. We can explain how to test things, how things work but generally refrain from making guesses.