One thing you can try is shutting down the DNS-343, removing all four HDDs, and then rebooting. See if that gets you to the web UI. Practically speaking, a RAID array created in one DNS-343 should be transferable to another identical unit, which would make this approach plausible.
Under normal circumstances, I would recommend that you backup your data before performing this type of activity, but that doesn't seem to be an option here.