Unfortunately I found your thread on adding another hard drive too late and actually tried formatting it next to the other hdd.
Adding a new HDD in the empty slot while the original HDD is still mounted is acceptable and should work. This is actually the prescribed method of adding a new HDD. Members of the forum sometimes opt to remove the original HDD before formatting only to avoid accidentally erasing the wrong HDD.
After you formatted the new HDD using this method, did you try accessing your data located on the original HDD before you removed it and placed it in a PC?
After I did this I attached my older hdd to the pc in a panic to see if I had lost all the files in there and could'nt find them so unplagged it again and back into my NAS with the new one sitting on the side waiting for a resolution.
If you physically installed the DNS-320 formatted HDD inside of a Windows PC, the PC will be unable to read any data. The DNS-320 formats HDDs using the Linux filesystem, and is not recognizable by Windows.
Unfortunately, if you tried accessing the HDD using a Windows PC, it's possible the Windows PC altered the HDD making it unrecognizable to the DNS-320 when you reinstalled the HDD. If what I wrote above accurately describes the procedure you followed, you may want to try the following course of action to recover your data:
DNS-320 - Data Recovery (Windows PCs)