Won't turn on unless

Hi guys,

I have a Apple MacBook Pro "Core i5" 2.5 13" Mid-2012

The problem with it is it won't turn on or off by the power button.

Symptoms are:

• It will only come on if I disconnect the battery and adapter and hold down the power button for a few seconds reconnect the battery and plug in the adapter, then it will start automatically.
• It will start if you then restart it. On the desk top.
• If you try to start it with the battery disconnected, you get the continuous three beep noise indicating bad ram connections (it has frozen before, crashed and gone to this state)

Once the battery is completely charged it won't start at all.