The TL494 should be fully powered and is generating PWM pulses internally, even with the PS is at standby. What prevents its output pins C1 and C2 driving external transistors Q3 & Q4 is the signal coming into Pin4, the DTC(deadtime control) pin. This signal is controlled via the TPS3510. A high voltage at this pin would force the duty cycle to 0%.
If you monitoring the voltage on this DTC pin to ground, you should see a high level(more than3.3V) when the PS is at standby. When you physically push the PC start button, this voltage should drop to near zero to allow the output pins C1 & C2 to drive Q3 and Q4. If the voltage do drops but there is still no output, check the pulse transformer T2 pin8 for voltage, and components R80, D9 and R11, then Q3 & Q4 and components around their base.