My macbook will not switch on with a battery

I plugged my macbook in and tried switching it on, it did not switch on. I took the battery out and tried again without the battery, still no luck. I put the battery back in again while it was still plugged in, took it out immediately and my macbook spontaneously switched on. If you unplug it, it turns off and will not switch on again unless you insert the battery and then take it out. What is wrong?