You need to add one more distinct possibility to your list; it wasn't changed often enough. Most all modern oils will keep an engine clean if they're changed often enough. If a car is driven very short hops with no chance to warm up, then 3,000 mile intervals aren't even adequate.
The best way to now get it cleaned out would be to use a universal grade oil, such as Delo, Rotella, Delvac or any other that is designed for diesels. These oils have more detergents. If you would drain the oil while the oil is at operating temperature, which is typically about 17 miles of driving, and let it drain for a while, preferably overnight, then put in your universal grade. Do this about every 1,000 miles for two or three oil changes, I'll bet you can then pull the valve cover and find things crystal clear.