In the sentence "The street lights are shining brightly at my window" there is no participle, only verb, "shinning". The word "brightly" is acting as an adverb, modifying the verb, "shinning" in the sentence. Remember, adverbs modify verbs, nouns, adjectives, or pronouns. It describes the manner, degree, extent, such as brightly describes in what manner or degree to which the light shines.
