Is it doing absolutely nothing when you press the power button? Do any lights light up or fans spin up?

Remove everything and just fire up the motherboard withoutout memory - just install the CPU and keep it connected to the monitor. If all is well you should get nothing on the display but you should hear a repetitive error beep and the fans should spin. Power it down ad try it again with the memory and see if it POSTs. Otherwise you can be pretty sure it's your motherboard or PSU that is at fault. Even with a dead CPU, you usually get some fans spinning but nothing else. What about your HDD(s) and optical drive(s) do they fire up?

If you do mean that absolutely nothing happens. Then you might be on to something when you say that the power button connection might be the problem. Do you have an other old case lying around? If so connect the power button from that case into your motherboard and see if you can power up using that. Check the front panel connections carefully as well as the system buzzer might be disconnected also.

You say you tried removing the CMOS battery? Does the board have a clear CMOS jumper? Try shorting the jumper and power up with the CMOS batter removed. Leave it for about a minute like this as it takes time for the nvram to completely clear. Next cycle power again and remove the kettle lead from the psu. Hold down the power button to get rid of any residual power. Put the CMOS battery back in and try powering up again - with just the CPU and memory and connected to the monitor (so install the graphics card if you have no onboard vga or otherwise use the onboard).

Can you try another PSU from another PC?

If that doesn't work then I'm out of ideas and I suspect the motherboard has been damaged - perhaps by a power surge.