I have a website developed in ASP.Net 2.0 that is throwing the error
"Exception has been thrown by the target of an invocation"
I'd suggest checking for an inner exception. If there isn't one, check your logs for the exception that occurred immediately prior to this one.
This isn't a web-specific exception, I've also encountered it in desktop-app development. In short, what's happening is that the thread receiving this exception is running some asynchronous code (via Invoke(), e.g.) and that code that's being run asynchronously is exploding with an exception. This target invocation exception is the aftermath of that failure.
If you haven't already, place some sort of exception logging wrapper around the asynchronous callbacks that are being invoked when you trigger this error. Event handlers, for instance. That ought to help you track down the problem.