The plastic button just presses a button soldered on a daughterboard. You can use it to power back on, if you can access it somehow. The power button is on the same side as the ribbon cables, so you have to be very careful when checking it (but I'm not sure if you can see anything from there). Also, the daughterboard which hosts the buttons use a ribbon cable connecting to the mainboard, too. Maybe you can check this also, if it has become disconnected.
Worst case, I guess I could remove the button and use something pointy to get to the button. The ear speaker blew out last week as well, so I suppose I at the end of the useful life of the phone.