Won't turn on unless power adapter is connected

Hi All. It seems that I made thing worse by trying to fix things myself. :) This macbook of mine one day just wouldn't boot up. Battery is full as indicated by its green lights. Upon pressing the power button, all I see is a blank black screen (back lights not turned on), no startup sound, no nothing. Fan is turning, HD is spinning, front white light on. Then within 5 seconds, it would seem to reboot, you'll notice this because you'll hear the sound of the HD would suddenly stop and the front light would turn off, but within a second or 2 would again turn on, still a blank black screen and no startup sound.

My first though was it could be something in the logic board short circuiting. So I went ahead and tore down the entire macbook to get the logic board out to clean it by a dry brush to get some of the dust out.

Put it back together, tried to turn it on, nothing. No spinning disc, not front light, no fan spinning. Green lights indicate ample amount of battery though. I went to get my power cable and plugged it into the macbook, then suddenly it turned on, fan and HD spinning as well as the front light is on, no screen display and startup sound though. This also wouldn't turn off, I had to pull out the battery just to turn it off.

Any suggestion on how to fix this is much appreciated.