Chevynut wins it. Pressure test the system, if you dont see it escaping from the intake, and it isnt going into the oil , then pull the plugs and crank it over. chances are you'll see it shoot out of a spark plug hole.
Be sure to check the oil to see if it is going there.
Chances are you have an intake leak that is just hard to spot.
Dont rule out a heater core. You will see that dripping from the A/C drain on the evaporator/heater core housing.
check it over good first as those are known for having intake leaks(and head gasket leaks
better to check and find it first BEFORE you tear it down, so you fix it the first time
Chances are the brown crappy looking stuff is degraded Dex Cool, GMs answer for the environment. Unfortunatly it turns to crap and starts to plug stuff up.Flush it well when you get the leak fixed and run good ol glycol.
Be sure to pick a low silicate formula if you can find it.Read the Jug, it should tell you on the back.