This sentence contains two dependent clauses: "When they told me", and "(that) I won the contest", the latter which serves as the object of the verb "told". The connecting word "that", if not explicitly included, is understood to implicitly precede "I won" and in either case functions as a subordinating conjunction. This sentence also includes two independent clauses, "I cried" and "I didn't faint", connected by the coordinating conjunction "but". The first dependent clause, together with its object (the second dependent clause), adverbially modifies the verbs of both main clauses.