If you are sure there was no disk activity at the time the logs won't show anything of use.
I think you have a rather larger problem than first appeared especially if you don't have a recent tested backup to fall back on.
There are a couple of things you could try,
1) do a factory reset - after copying your settings to something like a USB stick. This might clear the problem but, because we have never seen a case of a missing partition in any of out, or our clients, NAS boxes, I just don't know.
2) power off the NAS, remove the 2 TB drive and install it in a USB/SATA caddy or adapter and use a Linux based box to access it and do repairs as necessary to the partition tables. You might need a program like DFSee
http://www.dfsee.com/ with latest version available at
http://hobbes.nmsu.edu/h-browse.php?dir=/pub/incoming/ It is fully functional for a couple of months and has just about all you want to know about working with disks in the documentation - be careful if you use it in 'expert' mode because you could mess up what you have if you don't know what you are doing.