At the I/O menu, set input select to "Digital." This will record the Stereo signal to tracks 5/6, rather than the Stereo Tracks (7/8), which have better meters.
In the "Rec" menu, set "ST Rec" to the "Mix" setting. If set to Digital, the above setting in the I/O menu will have no effect.
Make sure both units are set to the correct sample rate and that you see a "DIN Lock" message on the DR-680. Also make sure your digital cable is working correctly.
If it's still not locking, you could try the V3's AES outputs (assuming you have proper cables). The 680 will automatically sync to SPDIF or AES formatted signals and I always found AES signals to sync more reliably.