I had the same thing happened to me. Twice.
When I asked, Nikon wanted I think $120 to get it fixed. Or more, I don't remember. The point is that I do not have the money to get it fixed.
So, I decided to try to fix it myself. And I did.
I did a bunch of research, and took my flash apart and put it back together several times, and I managed to not electrocute myself in the process.
Basically I found out that...
Oh, first: Disclaimer: I'm not some kind of certified technician, or trained in this kind of stuff. All I know I found out by myself, by experimenting and just generally being interested. The stuff I'm about to describe will FOR SURE void any kind of warranty, and it's also quite dangerous to do, considering that there is like 400V inside the capacitor of your flash, and you don't want that to go through your body.So I'm not responsible for any kind of damage that you or your flash or anything else might suffer in the process. In fact, I'm not responsible for anything you do. It's all up to you.Advice: Before you start poking the inside of your flash with soldering irons and screw drivers, DISCHARGE THE CAPACITOR!!!! You can find how to do it in the repair manual on Page-9.
(HERE is the repair manual PDF)
Or alternatively, you can... well, this is a bit dodgy, but considering that your flash is dumping all the charge from the capacitor every time you flash, you can just press the test button, and RIGHT after the flash fired, rip the battery door open. This will not allow the capacitor to re-charge again. (this does not work if your flash is not broken the same way as described above. In case you have a working flash, you MUST discharge the capacitor as described in the above PDF.)
OK, so basically I found out that there are 2 components inside your flash that can be responsible for the above symptoms. (assuming you already tried the 2-button reset and it did not work)
One of them is a little black transistor, called IGBT. (Insulated Gate Bipolar Transistor). This guy is responsible for cutting off the electricity at the exact moment in order to provide the desired amount of light. If this transistor fails, it will not cut off the power, and will let all the electricity through the flash tube, therefore you end up with a nuclear blast, and an 8 second recycle, not matter what setting you are on. (even if you press the shadow button). This component can be found in pretty much every modern speedlight. (I know that many Canon flashes have it, and the SB-800 and the SB-50DX have it too.)
To fix this, all you have to do is to buy a new one, de-solder the old one from the PCB-B in your flash, and replace it with the new one... It's much easier to say, than to do.
There are some slight differences between SB-800s. They have slightly different parts inside. The number on the IGBT in my older flash is CT40TMH-8 (data sheet PDF), and it's made by Mitsubishi. You can find it on e-bay, and order it. It costs about $6+shipping. It's quite good compared to the $120 that Nikon is asking for. In my newer SB-800 it was a CT40KM-8H (data sheet PDF), made by Renesas.
The other thing that can go wrong is the fiber-optic-thing-whatever-it's-called. There is a little fiber cable that attaches to a photo-diode on the BCB-B. This thing is being held in place with a little metal thing. if the fiber optic cable is not properly seated in the housing of the photo-diode, or if it's broken, you will have the same phenomena as described above. Full power pops, no matter what.
This is because this photo diode is responsible for seeing when the flash tube lights up, and by seeing that, it does it's thing and eventually tells the IGBT when to cut off the power. If this photo-diode does not see the light coming on, it will also not tell the IGBT to cut the power, and you end up with a nuclear blast again.
To fix this, you have to take the metal piece off of the photo-diode housing, plug the fiber in as far as it goes (basically all the way, until it stops) and then put the metal thingy back on. If it does not hold securely, glue it in place.
MAKE SURE YOU DON'T BEND THE FIBER. IT BREAKS VERY EASILY!
if your fiber is broken, you are pretty screwed, and you have to find a new one that is exactly the same diameter and replace it. But I bet that it's also cheaper than $120.
With that, your flash should work now!
I'd check the fiber first, to make sure that it's not loose, before ordering the IGBT. It could be that there is no need to buy anything, just put the fiber back where it's supposed to be and then it's all good.
I hope this helps!
And feel free to leave comments if you have anything to say about this.