You will need to remove the bottom cover, unplug the battery from the logic board, hold down the power button for about 20 seconds, then, while continuing to hold down the power button, attach the Magsafe charger then count to five. Release the power button then press it to see if it responds. You MAY have to repeat this a few times but this normally works.
Once it powers up, re-attach the battery to the logic board, while it is on(YES! I know you will be skittish about doing this but I have done it multiple times without causing any shorts or damage to the logic board.) and verify that the battery is now taking a charge.
The reason this happens is the logic board builds up an electrical charge that causes the unit to not release the power from the board, when the unit is turned off. Windows units do the same thing. You have to drain all residual power.
Hope this helps.