I use the Turbo 2x2 batteries with the T5D-r. I suddenly started having the same issue regardless of which battery it's connected to.
Test firing the flash head manually does work. Assuming in this case that it's either the D700 hotshoe, or the TTL adapter (a replacement adapter has just been received and will be tested with the setup shortly). The camera body is due for a "once-over" at Nikon anyway, so will be getting that end of theings checked as well - just in case.