Console Randomly Turned Off and Now Won't Turn On

Console turned off randomly while playing a game. Now the console won't fully boot.

Pressing the power button the first time causes the console to beep and nothing else. Pressing the power button a second time has it appear to attempt to boot up. You can hear the fan and disc drive. You'll see a blue light for around 5 seconds, then it'll become a white light for around 20 seconds, and then the console powers itself off.

During all that, the monitor does not have a signal.

Holding the power button for Safe mode sometimes does work. When it does go to safe mode, pressing many of the options shows the screen freeze and turn off after a few moments. When holding the power button doesn't go into safe mode, you'll hear a first beep after holding the button for 7 seconds, then a second beep after 7 more seconds, then after another 7 seconds the console automatically turns off.

I've tried unplugging the console for a few minutes.

I tried a different wall outlet, different power cable, and replaced the PSU with a new one.