All Ouya Support entries go into this catagory.
This is also another ugly worst-case Ouya Support issue. Where the Ouya will either completely lock up causing the HDMI signal artifacts since it just lost it's clock timing even though power is still being supplied to the LCD or flat-panel TV.
This problem I've been hearing it pop up from a handful of users but never really experienced it myself which is the flashing power issue. In this scenario, it is assumed that you get at least some form of video on your screen when you are holding down the power button such as the orange (U) logo upon power-up. Perhaps if you hold it down long enough it comes all the way up to the main menu. If you are not even getting video then it may be something more serious then a simple power switch issue.
Before you panic and think of the worst-case scenario that your Ouya is totally gone it may not be receiving no power from your power supply. I had a friend which had a defective 12v power supply for their Ouya, I took a voltmeter to the barrel plug of his power adapter it was was only reading something like 0.6volts! Test out your Ouyas Power supply first with a multimeter if you have one. If it is defective you can pick up a universal PSU from radio shack or eBay so long as it delivers an output of 12 volts and 1.5 amps. If the amperage is less then 1.5 amps the Ouya may have issues crashing while playing games.
The burning Ouya is a bizarre Ouya Support issue and it happened not on my developer Ouya, or my Kickstarter Ouya but an Ouya that I got from a retail outlet like Target. My router is loaded with DD-WRT and I was able to detect all of the Ouyas in my house are constantly sending data over the network (some more then others depending on how many background services you have going). 
This is by FAR the most annoying feature of Ouya where you have to enter financial information such as credit cards into a device that can be easily stolen or compromised due to physical presence. The only good news to offer is that you no longer HAVE to use a credit card to generate an Ouya account.