He went to London and sold his plays, and since his style of writing was unique, so people were interested in him.
There are no dependent clauses in that sentence. Both "Vampire Diaries is my favorite show" and "I also love True Blood" are independent clauses because they contain a subject and a verb, and could stand alone as a sentence. "but" is a coordinating conjunction that joins the clauses, meaning both are still independent. The coordinating conjunctions are For, And, Nor, But, Or, Yet, and So ("FANBOYS"). If a subordinating conjunction (such as "although" or "however") were to join the clauses, the clause containing the conjunction would be the dependent.
