Not familar with the detailed workings of the CLS system but from the description it sounds like it might be hot shoe contact related. That's a problem that plauges the Canon 580exII.
Check /clean hot shoe contacts, that the hot shoe on camera isn't loose and that all the pins on the flash are moving freely.
Are you sure the camera is not in commander mode. Two commanders i.e. sb800 and camera might be in conflict.
I vaguely remember a similar issue when I had a D70 years ago.
Chuck, I tried to clean the hot shoe contacts and all the pins seemed to be ok.
Erik, I've set the D700 on each of the different modes it has and I seem to get the same result, so I don't think there's a conflict there once the sb-800 is on the hot show.
During more testing, I ran into something else that's weird. I noticed that every once in awhile the 600 would fire correctly under this scenario, so I tested 20 pops and 65% of the time I got the error beeps, 20% of the time it fired like it's supposed to, and 15% of the time it did neither (just sat there).
One more thought for you. I just got through reading a thread here ( I think in the Nikon forum) about D700's with hot shoe issues, causing intermittent flash problems. See if you can find that thread and perhaps notice any similarity with your problem. If so, your 700 might require a trip to Nikon repair. Good luck, and hope it turns out to be something simpler than that.
