Before you RMA the DNS-320 - one possibility of it seemingly not starting up is simply that it doesn't like the (corrupted?) filesystem it sees on the drives...
So, a couple of quick tests you could try
(a) Do the drives actually spin up in the DNS-320 - even if the blue "left" or "right" LEDs don't stay on? If you can't hear the hard drives over noise of the fan, try using the old screwdriver trick; place the blade end on the end of the drive's chassis and put your ear to the handle.
(b) If you have access to a spare SATA hard drive that you can "wipe", use a disk erase tool to do a full wipe (e.g. write zeroes in the whole drive) and put that in the DNS-320. If that one spins up, the blue LED stays on and you can format it, then the issue might be due to data corruption, not a hardware failure... after using NAS data recovery to get back your lost data, you could try doing a full erase on the drives and put back into the DNS-320 and see if they start working again.
FWIW, although not in the DNS-320, I have had a PC BIOS not recognise a hard drive when there's been corrupt junk on it; doing a full erase to "all zeroes", the drive was then detected OK and has been working ever since. So the same kind of thing could be going on in the DNS-320?
Regaerds,
Richard