Applying occam's razor, it seems most likely that N844AA crashed to ocean or deep jungle. Any other explanation (dissassembling to parts, drug running, ...) and people would have seen it. And since this 727 became famous, at least one person seen would spilled the beans during the last 10 years.
But that would only be the "what happened" part. There is no convincing simple theory for "why it took of".