hmm thats tough, it could be a few things (PS, switch on the case, mobo). if i had to guess i would eliminate switch on the case and narrow it down to power supply or mobo. either the power supply stops supplying the mobo with power or the mobo stops carrying the power for whatever reason. i would try replacing the power supply first and if you get the same problem than its probably the mobo.

also make sure the heat sink hasn't become loose, and to test the power button just unplug it from the mobo and touch the 2 pins with a paper clip.

Yeah, you can test the switch by shorting the power pins (a jumper works well) on the mobo.

IF YOU HAVE AN ATX (if it's a Dell, HP, or any other non homebuilt machine don't try this), the PSU can kind of be tested by shorting Pin 14 (green lead) and a Pin 15 (black lead) on the PSU connector with a paperclip.  Unplug the PSU from the wall and the mobo, put in the paperclip, plug into wall, see if the PSU fan spins.