My NAS not responding

I don't know a lot about the 626.  With older ReadyNAS, the default display (programmed into the display panel) was just "ReadyNAS".  It seems plausible that the newer ones have "Netgear Storage Welcome" as the default, as it seems to display too fast for the processor to create it.  If that is the case, then, as is the case with older units, it means there are a lot of things that could cause it because it doesn't even need to complete POST for that to display.

One of those things, and one of the few replaceable items, is the power supply.  And that generation of NAS is getting old enough that a PSU is a reasonable suspect.  That ReadyNAS family uses a supply that's similar to the ones the 4-bay legacy units use.  That is, it's a Flex ATX form factor with a modified pin-out.  But unlike the ones for the legacy units, it also has the 4-pin CPU power connector and does use the PSU fan.  There is now a seller on eBay that has a compatible supply for sale, or you could modify the pin-out of a standard one.  But, it's a risk doing so as a troubleshooting step, since a whole lot of other (mostly non-repairable) things could also be the problem.  You could fashion an adapter cable for a standard ATX12V supply and use it externally just to see if that's the problem or to power it long enough to recover data if needed.  But that's really only a good plan if you already have a power supply you can use.

Better is if you have a way to measure the voltages from the supply when it's connected.  You can check them with it disconnected as well, but that's an inferior test to while under load.

Another possibility is the RAM, and that is replaceable/expandable on a 626.  See this thread regarding memory for the 626: Upgrade-ram-in-readynas-626x.

The CPU is a BGA, so no replacement/upgrade possible without specialized tools.