The power supply probably died when no activity was happening . . . Yet really not known.
The original power supply was rated 3A on the 5 and 12 volt
rails. I was unable to locate a 3A PS so the 6A PS was a suitable
choice as a replacement. I see the 323 A and B models have the
same power supply.
The power supply from Amazon, Arcity Switching Power Supply (+5V/8A +12V/8A +24V/3A) for Multi Machine Video Game Cabinets and Cocktail Console DIY Adjustable Durable New . It did not come with the needed cord and plug. I still had the 5V side working so was able to see 5V Red, 12V (not working) Yellow and Black/Copper 0V or Grd. (Confirmed with drawings and voltmeter in plug.)
Cutting the cord, an inch from the old power supply, and attached it to the new power supply (about 1 meter of cord and power plug). The shield was being used as 0V wire #2. Covered bare copper shield with shrink sleeve.
I currently have it stuffed into a space between the bookcase and wall. A few temperature checks while the rebuild was happening revealed no excess heat was being generated, easily less than 30C being felt.
Photo attached.
About 20 months later and the NAS is used weekly to backup computer and phone.
Good luck with your project.