Simple transistor for switching a computer power supply
The problem seems to be as obscure as expected. Not related to having the supply loaded or anything. I am simply using a capacitor to smooth out the signal to the base and the circuit works. Discovering further, this external power supply is intended to be earthed and wasn't. Even still, the capacitor seems to be necessary for startup to be successful.

I edited the above schematic, adding the 187uOhm resistor to pull the base down and open the main circuit, also to discharge the 680nF capacitor. With those the circuit works well, controlling the ATX PSU with on and off signals.