Presuming the DNS-323 was physically damaged and the HDDs and JBOD are still intact, you should be able to drop the two HDDs into a new DNS-323 without any issue. The DNS-323 formats HDDs using the Linux filesystem and the way the DNS-323 formats RAID and JBOD arrays is somewhat unique, so you are likely to encounter issues trying to install the JBOD into a different model NAS. Even within the D-Link family, D-Link clearly states that HDD configurations created in early ShareCenter models (such as the DNS-321 and DNS-323) are not compatible with the newer D-Link ShareCenter product line, so the likelihood of successfully dropping the array into another brand device is probably slim at best.
If you plan on dropping the two HDDs into a new DNS-323, please make sure the firmware of the new device matches what's currently installed in your legacy DNS-323, and clearly label the HDDs with a magic marker so you install them in the same order as the original device.
Another option is mounting the JBOD in a Windows machines and using special software designed for Linux based RAID recovery:
DNS-323 - Data Recovery (Windows PCs). . . And I would be remiss if I didn't stand on my soapbox and state the importance of maintaining at least one backup of your critical data on another physical device.