Well - first off you may want something smaller than a 1K resistor to put the 2n2222 fully saturated (maybe 470 ohm, or 330 ohm); but try the 1K first, can't hurt.
I am not sure why you are connecting it to one of the analog input pins, unless you have no other pins left over, and you intend to set the pin to use it as a digital output...?
As far as the "PC Neg" and "PC +5V" - I don't know what these are. If your PC is an ATX power supply with soft-power switching (that is, there is a small momentary pushbutton that connects to the pins on the motherboard), then what you need to do is determine whether, when those pins are shorted (as they are by the pushbutton), whether one pin is being pulled low or high (and if high, what that voltage is - it may be 3.3V and not 5V, for instance). I don't know what motherboard you are using, or what the pins are labeled, or how they work - but you need to determine this first.
If you -are- pulling the pin LOW, then your circuit may work fine; in this case, the wire you have labeled "PC Neg" would go to the "ground pin" of the motherboard soft-power on pin set, and the "PC +5v" would go to the other pin in the set.
But you need to verify this information first! Otherwise you risk damage to the motherboard as minimum. It still may be more prudent to use that 2n2222 to control a reed relay, and then put the contacts of that relay across the power-on pins of the motherboard (believe me, a reed relay does not make a loud click sound).