Apologies in advance if these are too obvious a set of questions:
1) When you selected bkt mode from the front bkt button you selected the bracket set and it was displayed correctly in the viewfinder correct?
2) Unless you have continuous shooting turned on the bracket set will shoot one shot of the series per click - not the whole series. If continuous shooting is on, hold down the shutter and the series will fire.
3) If focus priority is set, but there's nothing in focus, the camera won't fire.
If the battery has enough power to shoot at all then it'll shoot a bracket set too. Ignore the battery indicator and select battery info from the menu and you'll get a much better view as to whether you have enough power to shoot. It takes a LOT to run down the D700 battery and I don't think I've ever had it refuse to shoot - if the battery is so low it won't shoot, it's flashing and not doing anything.
Hope that helps.