Ok I am saying if you think there is a short circuit, but you can't find any hot parts, chances are its a part on a heat sink, or with a heavy ground plane.
For high voltage power boards you really want a thermal camera that can point you in the right direction. Usually bad welding machines have blown parts.
My broke welder had clear signs of burn damage. Did you check perhaps to inspect the parts with a mirror to look for a cracked transistor? They often blow a corner off or something like that and look mostly OK
This one looks really simple. You could replace every single part fairly cheap, its always an option
My hunch is something bad with parallel MOSFET. I would just buy a dozen on digikey and give it a shot replacing them all lol, for 20$ + thermal grease. Chances are it might be a cheap welder with counterfeit parts (suspicious this is from amazon) and you might improve the thing. Plus, its kinda safer then probing around those. And you can probe most of the diodes too.
With parallel mosfet it might be complicated to try to determine if one of em is acting up, their like $2.95 so is it worth it ?
A good machine would have factory made IGBT bricks for this purpose. Parallel FET is alot cheaper but yeah who knows what can happen there!
I can ensure you, that probing those FET near the heat sink while its running is perilous. If you wanna try to do something there, get a fluke insulated grabber hook, turn off the machine, make sure its safe, connect the hook, measure, and repeat for every single measurement. Probing there while its on is the risky part for this machine. Those TO packages near BIG heat sinks are recipe for short circuit trouble