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all you would be doing is cutting the power on and off by adding a switch to the green and black wire shown I am not positive but the transistor and the resistor would be needed so that you would have 5volts on stand by and i am sure its there for a reason.
If it's an ATX PSU it has a 'standby mode' which is really just everything is off inside there but the 5vsb line. When PS_ON is grounded the PSU turns on, when it's not grounded the PSU is off, aka in standby. Make sure you have the EBC wiring correct on your Transistor. You should also have another Resistor from the Base to Emitter (roughly 10 times what your Base Resistor value is, so ~150k) so the Transistor will turn off when it's not being biased to turn on.
The Base Resistor is a current limiter. The one you need to connect between the Base and Emitter will make sure the Transistor cuts off. If you're just snagging random parts, are you sure the Transistor is an NPN type? and that it's even good?
Assuming with electronics is a good way to damage something at best, or yourself at worst if it explodes from being connected someplace that it shouldn't be, and that's why parts, have part numbers.