readynas314 not powering on

Your NAS does not have an internal power supply like many of the older models as in that video.  If it is the power supply that's the issue (and the likelihood it is is high), that's a good thing -- less expensive and easier to replace.

If you do replace it, here are some pointers:

• If the vendor doesn't state the current (or wattage -- 7.5A @ 12V = 90W), and especially if they blur out or "strategically" cover the label, avoid it like the plague -- it's probably an underrated supply.
• It's best to avoid supplies listed strictly for LED lighting.  They often cannot handle the inrush current of a NAS and may not be the best regulated supplies.  Look for one that lists a NAS or cameras, monitors, and similar equipment.
• Be mindful that not every power supply with a 4-pin connector uses the same pin-out.  The Synology NAS use the same pin-out, so you can look for that if ReadyNAS isn't listed.

If you are looking for a specific recommendation, I have used the TAIFU 4-Pin 12V 8.33A  supply sold on Amazon.  It has a little extra power, which can be a good thing.

While your NAS does not have an "internal power supply", it does have internal circuitry that converts the 12V to the voltages necessary to run the NAS.  Those, unfortunately, are not repairable, as are pretty much everything inside the NAS.  (Well, they might be repairable, but Netgear has provided no schematics to make it easy to do.)  So if a replacement supply doesn't fix the issue, you are likely out of luck unless it's just a bad connector.