I hate to lead you on a second goose chase, but those capXon electrolytic capacitors are known junk.
forums at Badcaps.net has good for advice on capacitors and repair too.
I would suspect the PFC controller start-up power, U1 Vcc is pin 8
FAN7930C which needs 12-13V to start. So C10 is suspect but I cannot see around D8 what is powering the PFC controller IC.
My guess is your touching the scope probe might give an extra blip and raise Vcc so it can start up.
You can try run it for a while, cheap electrolytic capacitors seem to act up cold and in their last days, work somewhat when warmed up.
I would test/replace all the electrolytic capacitors in this PSU as capXon is pretty bad.
Best to clean off flux using IPA and cotton q-tip, the high voltage needs a clean PCB.