The specs don't mention a 2 wire as such. Maybe a SATA power?

One issue with systems that don't power up correctly is problems in the
standby circuits. Or you could have capacitor problems. (google search
for "bulging capacitors".

You could also pull the power up connectors off the board and see if
shorting the pins with a screwdriver will bring the system up. The power
up switch hits the standby circuits on the M/B and those circuits then
signal the P/S to come up. IIRC, it is the green wire going to 0 that
brings it up.