Review the original item:
For two weeks, Todd refused to go to his accounting class because Professor
Gastineau would not allow students to wear hats,
under no circumstance would Todd allow anyone to see how badly the
barber had butchered his hair.
You chose the correct way to fix the error:
For two weeks, Todd refused to go to his accounting class because Professor
Gastineau would not allow students to wear hats,
and under no circumstance would Todd allow anyone to see how badly
the barber had butchered his hair.
For two weeks, Todd refused ... begins a complete sentence. Under no circumstance would Todd allow ... starts the second complete sentence.
A comma and the coordinating conjunction and will fix the problem nicely.