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I have a D200 tethered pretty much full-time in my studio macro setup. Through thousands of images, I have never had problems such as you're describing. Also, I've used at least four or five different computers for this. But I did once have a D700 not be recognized; it was an intermittent problem, occurring with just one computer, and I simply switched to another computer rather than troubleshoot it.
For tethering, the D200's USB mode should be set to "PTP." That the camera is not recognized by the computer in this mode is the problem you need to work on. For that, I have no magic solution. Thoughts that come to mind: Try a different USB cable (preferably a short one, until you have the problem resolved). If you are connecting through a USB hub, eliminate it. Also, try different USB ports on your two computers; on the desktop computer, prefer the ports in back of the computer, coming directly off the motherboard.
What operating system are you running? I've had an easy time with XP and Windows 7 machines. No clue about Vista or any MacIntosh OS's.
What camera control software are you using? I use Nikon Camera Control Pro 2. If you are using ControlMyNikon, I'd suggest downloading the free trial of Nikon Camera Control Pro 2 to see if the problem goes away. (No disparagement meant of ControlMyNikon--just looking to isolate a variable; I've also wondered if Nikon includes some camera drivers with their software that may not generally be available.)
I don't know if any of this helps, but for sure, tethering a D200 can work very well. Good luck!