PlayStation 4 is experiencing a few teething troubles, but Sony has made a troubleshooting guide available for at least one repeat complaint - issues accompanied by flashing blue lights.
If you're experiencing no video or audio output, blinking blue lights, and the console switching itself off, you should take a look at the guide posted on the PlayStation forum.
The problem may be related to the power supply or hard drive. Sony suggests a full restart, which you can trigger by holding down the power button for seven seconds, then unplugging it from the power supply and checking all your connections. If that fails, you can check the HDD following the steps on the guide.
If that doesn't work, you can try rebooting in safe mode; there's a step-by-step guide to that, too.
Users have reported updating their TV firmware can cause issues, too.
The PS4 uses lights to indicate a variety of issues; visit PlayStation Support for a guide to what they mean.
Despite these issues, the PS4 has had a great launch, with over 1 million units sold since hitting North America on Friday.