Remotely Turn on Computer

I have seen various projects using an old cell phone + skype and then an arduino sensor to detect light or vibration and start the computer. I am relatively new to Arduino, I have only written simple programs that play with leds or turn on a motor and basically drive it around with wheels.

Here's my questions:
-Is it possible to bypass the phone, and somehow "call" the Arduino with a wifi sensor?
-If not, just calling the phone would most likely have it lighting up or vibrating periodically due to a missed call. Correct me if I'm wrong but wouldn't this cause the system to keep shutting off and turning on.
-I understand that just connecting the two wires on the + and - PWR to the motherboard will start the system, how would something like this work on the Arduino without physically pressing a switch, what module would I use for it?

Takachsin:
-Is it possible to bypass the phone, and somehow "call" the Arduino with a wifi sensor?

If you have a WiFi module, you could write a small server that you connect to. There are lots of examples on doing something like this.

Takachsin:
-If not, just calling the phone would most likely have it lighting up or vibrating periodically due to a missed call. Correct me if I'm wrong but wouldn't this cause the system to keep shutting off and turning on.

I guess that depends on how you design the system

Takachsin:
-I understand that just connecting the two wires on the + and - PWR to the motherboard will start the system, how would something like this work on the Arduino without physically pressing a switch, what module would I use for it?

A transistor.

Thanks for the quick response!

Are you talking about something setup like this http://arduino.cc/en/Tutorial/WebServer?

I have a NPN BJT transistor, will that do the job? Or do I need a JFET?

The power control interface is most probably just a simple logic button interface just like you have on the Arduino. It may be active-low (pull-up resistor), or active-high (pull down resistor), so you'll have to probe and experiment, but it won't be any more than 5V (the ATX power supply gives 5V standby power for the power switch circuit to work).

As far as the power supply goes, it has a pin which is at 5V normally - link it to ground and the PSU turns on. Separate it from ground and it turns off. It's a green wire on the main ATX plug usually. You could take advantage of that instead.

The purple wire on the ATX power supply is the standby power. You could theoretically run your Arduino off that power (if it will give enough current - I don't know what its limit is) to save having extra power supplies and things.

Or, if your motherboard supports it, put an ethernet shield on your Arduino, and use it to send a wake on lan. Or even use WiFi, and use wake-on-wireless-LAN.

I haven't fully grasped your requirements, but if you just want to get a computer to come to life one option would be to send it to sleep mode instead of powering it off, and then have the Arduino emulate an HID and send it a keyboard event to wake it up.