I'm a D300 owner and luckily have never experienced any problems with the camera except operator error.
With respect to the 'ffffssst' sound it made when you pushed the battery harder in sounds like some sort of short that has now killed it totally.
You mention that you use the Kenko Teleconverters and wonder if the problems you are experiencing are specific to when these are fitted ?
I mention this because I have read various articles where concern is raised at the intermittent failure of certain functions due to the loss of continuity of electrical contact caused by slight play in the mounting. Although these concerns were with regard to the Kenko Tubes and the affect from heavier lenses it is something to be aware of.