Are you sure the momentary contact switch you're using is good? Have you tried shorting the ATX power on contacts with a screwdriver?

the switch is not the issue, also the solder joints on that ATX connector look fine.

Give this a try: https://www.youtube.com/watch?v=nYb7UaWip8w

well, good thought, that indeed caused it to start up. tested with the switch again to be sure, and nothing.

as per a comment on that video, i tested the 105 resistor connected to the soft power switch along with an adjacent 474, and some other ones in that area, which are all fine. there aren't any resistors at the ATX connector as far as i can tell. well, i'm almost a bit wary of working on this, because patching up a cut trace on a slot 1 board one time resulted in some magic smoke from the PSU...

Worst case scenario, you could rig up a momentary contact switch to the contacts in the ATX power connector. I've no experience with repairing traces on motherboards, but I know there are other members of Vogons who do, so if you should be able to find a broken trace that's the cause of this issue make sure to add that to this post or start a new one seeking advice on the repair.

if it works with the at connector but u dont want to us and old at psu why not just use one of those at to atx adapters on the at connector. they don't cost to much and better then messing about and maybe breaking the board totally if u don't know how to fix the issue with atx connector. other then that send it off to someone who knows more about fixing that type of stuff.