Console randomly shuts off after an hour or more of use

I have the launch edition PS4 (my first mistake, I know), and right when the 1 year warranty was ending, it started emitting a loud hum and then shutting itself off about 30 seconds after the hum. I contacted Sony - and was told I was out of warranty, too bad. It got so bad that after reformatting the hard drive three times, along with everything else everyone told me to do, that my console would shut off as soon as I turned it on. I bought and installed a new power supply - through this site, no less - and while it's working much better, my PS4 will still do that quick, loud hum, the screen will flash white, and if I'm playing a game, I can't control my characters anymore. Then the console shuts off. If I've had the console on for a few hours, then put it in rest mode for an hour or so, then power it back up, it shuts itself off, too.

Does anyone have any idea what the real cause of all this stupidness is? I just want to play my $*#& games and watch some movies without always having to restart and lose all my progress. I want the console I paid for, not a shiny brick! Thanks.