Q: Problem with transmission and battery.

The brown junk is your radiator is the result of the dexcool coolant that General Motors uses in their vehicles. If the coolant is not routinely flushed out and replaced periodically it will break down. If air gets into the system it will react will the coolant and for the lack of a better term, turn into mud. This clogs the system and can cause havoc with your radiator and heater core. If it is bad enough both the radiator and heater core will need to be replaced. I would ask for help from a mechanic to check what code is set in the computer and to check the condition of the battery in your vehicle. It is likely that the battery is bad, or the alternator needs to be replaced. The mechanics at YourMechanic will be able to check over all your concerns and get your vehicle fixed up.