How does the brain create original thoughts? Since the generation of thoughts requires the coordination of various parts of the brain, how does the brain know which parts to activate to develop unique ideas? Does the brain randomly activate its various regions until it happens upon a unique thought? 

Is the creation of unique, original, and creative ideas a function of the brain alone, or does the brain require an outside stimulus to engender creative or unique thinking?

There are many instances of great thinkers arriving at groundbreaking ideas from mere observation of nature and society. For example, Einstein developed his equivalence principle by thinking about elevators (mundane, everyday machines).

So, in summary, does the brain need outside stimulation to think imaginatively, and how does the brain coordinate its different parts to generate unique ideas?
To understand how the brain "knows" what to do, we can look at how children learn language.

At first, children randomly create all kinds of sounds, including those that aren't part of the language(s) spoken in their environment. Parents and other people react to these sounds, repeating them, speaking their language, smiling, etc., and the children in turn react to these reactions to their sounds, learning which sound elicit which reactions (e.g. which sounds lead to a smile, which sounds are ignored, etc.), until they slowly begin to build a repertoire of sound and "pre-words" which give the most pleasurable results.

With time, children learn to recognize parts of the language spoken in their environment and begin to emulate these sounds, learning their first words, and eventually to speak.

So what we have here is a brain creating random behavior (in this case with the speaking apparatus), and learning from the effects this behavior elicits in the environment which behavior leads to the desired results. Whatever happens in the brain when a desired result is achieved, is stored as the "internal behavior of the brain" to do to achive that result, e.g. what to say to get that ball.