This is a completely invalid experiment. Look, nobody is going to pay anyone five or six hours to check for every conceivable explanation, because that would put the bill @ $175+ even before you've fixed anything. $300 computers are NOT $15K automobiles.
Wires (secured with hot glue and snap-fit terminals) are NOT just 'coming off' on their own inside a computer case. Someone had to be inside there mucking around and pulled them off. If you fail to inform the technician that you were inside the PC mucking around, there is absolutely NO reason for them to suspect that highly secured wires would be leaping off terminals on their own.
What you tell the technician can affect their troubleshooting priority and mindset. If they haven't found the problem within the amount of billable time that 95% of persons are still willing to pay for a troubleshooting fee before you've even fixed their computer, which is at most about 1.5 hours, and the computer is completely non-op (will not even POST), you're going to tell them "probably the motherboard or PSU, maybe both".
But then I would also not tell them its definitely this or that, either. I'd just straight up tell them, "I think its this or that but I can't be sure because, you know, I don't want to run-up the bill to half (or more) the value of the computer just to definitely pin-point the problem."