You guys are probably right….faulty motherboard. There are tools that will test the power connector on the mobo, but the easy way to do it is if you have a working TR. You can swap out various parts to test for the point of failure. The symptoms do sound as if the mobo is fried tho, which make sense. I’ve had to replace enough mobos in my lifetime to know that manufacturers are generally willing to accept a high level of variance in the quality control process.
I would poke around e-bay or similar venues to see if anyone is selling an old TR. Isn’t there also a Sony Parts website? Unfortunately you’ll probably have to look for and buy the official sony mobo as i’m not aware of any manufacturer that produces a similar form factor.
Good luck.