My iPhone won't turn on unless its plugged into a wall charger?

My first issue is, my phone won't turn on unless its plugged into the wall. When it finally turns on after being plugged in it tells me my phone needs to be restored and that it can't make or receive calls until so, well great but, when i unplug it from the wall it immediately turns off and will not turn on when plugged into my computer. I've tried different USB cables but none of them work.

Your battery is messed up. If you really need to restore it, try plugging it into your comp then turning it on since it will charge while its plugged into the comp too. From there, i think you can do what you need to do in order to restore it.

So like my iphone4 fell turned off, and I tired turning it on but it won't unless I plug it in the charger?