Review the original item:
Slouched in his seat, Michael tried to pay attention
the problem was that Nina's smile before class was distracting him
from Professor Tyson's grammar lecture.
You chose the correct way to fix the error:
Slouched in his seat, Michael tried to pay attention.
The problem was that Nina's smile before class was distracting him
from Professor Tyson's grammar lecture.
Michael tried to pay attention is a main clause. The problem was is the second main clause.
You are always correct when you use a period and a capital letter between the two main clauses that create a fused sentence.