Sounds like a general hardware failure, if there's no sign of a component having failed, get a multimeter/voltmeter and check connections. It's tedious but pretty much all consoles are mass-produced in China, and Chinese manufacturing companies are filthy and try to save as much money as possible. The problem in this case is that the console runs a hardware check before turning on, and the check is failing, it's likely due to a hairline fracture on a soldering joint, this is the case with most current-generation consoles because they're made with lead-free solder, which is more prone to invisible hairline fractures after repeated heating/cooling, which happens often inside the case of a high-performance console. If you're handy with a soldering iron and a multimeter, you could spend a few hours checking the connections to the chips and other components.
If it's not a problem there, then it might be a failure of a copper track on one of the circuit boards, in which case you could technically solder a bridging wire over the failed area to fix the machine. I must urge you not to mess with the motherboard if you don't know what you're doing though, you could forget things up further.
You could just send it back if you don't fancy spending hours checking every tiny connection though, as long as you haven't opened it up or used any form of jailbreak, it should be covered by warranty.
Seriously, I don't know why people keep the default cases for their consoles, mounting a couple more fans and heat sinks can prolong console life quite a bit if you can keep everything cool enough.
