Can you edit you're post and remove all the blank lines at the end?
(septillion above also mirrors this, and gives a good idea to use a molex connector to detect when the PC is on or off)..
Yep, it's a non destructive way.
when sleep or hibernation mode as well.. is there a difference? or a specific wire to use then?
In sleep the system is brought into a state of low lower but not powered down. So the PSU (and all power rails) stay powered on (fans keep on spinning as well). In Hibernate the system state is written onto the hard drive and the system is powered down (PSU powers down except 5V stand by) so it just looks like a power down.
* There is always a constant +5v ("standby") source .....correct?
- what line is this on the PSU pinout chart above? (The purple +5VSB line?)
- connecting to the motherboard USB is done through the header pins then? (and this stays constantly on?
I dont recall having my computer OFF and being able to use a USB port to power anything for example?)
You can indeed use the header. You have to loop in the manual for which one stays powered on. And on some (like mine) I can set it in the BIOS for some USB-ports. But on modern motherboards there's almost curtain a USB-port that can be configured this way.
* The rest of the +12v, +5v and +3.3v rails turn off/go dead.. when the machine is powered down
- do they stay 'on' when the machine is sleep mode?
Shut down or hibernate => go off. Sleep or stand by => stay powered on
- how can I tell or what wires in the above pinout diagram are to/can be used for checking when the PC is powered on or off? (Any of the remaining +5v/+3.3v rails....correct? doesnt matter?) And what is the difference between using one of these +5/+3.3v rails to check when the machine is off or on, vs the PC_ON (green) wire?
All power rail wires can be used but if the Arduino runs on 5V is would make sens to use the 5V rail. The PC_ON line is the line that's pulled LOW by the motherboard to tell the PSU to turn on. You can use it but you would have to modify the ATX connector.
- how then, can I tell or what wires should be used when the PC is in sleep mode?
Sleep is a bit hard because everything stays powered on. But on most (don't know if it's all, don't use sleep...) the power LED is flashing slow instead of being on. If you want you can check this but it's a bit harder. (If the power LED is blue it's possible because you have 3V but with a green LED you can't because 2V is to low for the Arduino. You can connect the POWER_LED line only to the Arduino and let the Arduno power the LED via a resistor though.) But I don't think that necessary because all the fans are powered on in sleep.