I'm sure the carbon was due to the bad EGR valve. Without the EGR the only thing that really goes through the intake plenum is air.
The EGR valve's primary purpose is NOT to reuse unburned fuel as is commonly thought. The EGR's purpose is to cool the combustion event, thereby reducing NOX emissions. It does this by introducing exhaust particles into the intake stream, allowing advanced timing by adding broken down and expended fuel atoms which will not burn again. This reduction in the amount of a useable air/fuel charge reduces combustion temperatures. This results in higher fuel mileage, especially during extended periods at cruise speeds. Other benefits are more advanced timing resulting in more power.
The downsides to the EGR are it can gunk up the intake tract of the engine severely, especially if the valve sticks open, allowing extreme amounts of exhaust gas into the intake.
This is probably what happened in your case.
Hopefully the replaced it under the Federally Mandated Emissions Warranty.
