Questionhow do you know if a 3800 motor has a blown head gasket
AnswerYou'll have either coolant in oil, oil in coolant, exhaust gasses in coolant or an obvious leak.
Best advice, take it to a good shop in your area and have them check it with a block tester, which is a liquid they put in a special tool, and "suck" gas from the radiator. The liquid is blue, and in the presence of exhaust gasses it turns green to yellow.]
Hope this helps
God Bless
PAwl