When the butten broke, I tried to push the contact on the board but still no power. Do I need a new power board??
Can this be fixed?

It is possible, although unlikely, that you would need a motherboard.

You could try picking up a replacement switch online or at a parts shop. You could also just cut and strip the wire and short the wire to toggle the power on or off though since it's just a simple switch. But before doing that, look closer at the switch on the case and make sure that the wire is connected securely to the motherboard. Also check to ensure that the plastic button is actually pressing down on the switch which is probably attached to the metal chassis of the tower. This would be located behind the plastic cover over the front of the tower.