Hi Brian and welcome to the forums.
If you replaced the power supply, sounds like a bad solder joint and/or loose connection in the console somewhere. I don't know how much you know about electronics, so don't know if you can fix the problem yourself. Disclaimer: I am by no means telling you to crack open the console and go digging around in there. You can damage the console more and/or severely hurt yourself. Don't do this unless you are qualified.
I would give service a call and maybe they can help you. Sorry I can't be of more help.