The answer is:
The letter from the sweepstakes company began, “Dear Finalist;” it went on to tell me that I might already have won $10,000,000.
In the sentence given, the introduction of the quotation must include a comma. Moreover, because it is a compound sentence that contains two independent clauses, they can be joined with a semicolon or a coordinating conjunction. In ths case, the semicolon is placed within the quotation mark.