A. She got offers to sing from a number of music directors.
B. Consequently, today her name is all over as a popular singer.
C. However, she was really reluctant to give auditions, which delayed her entry into the field music.
D. Not only was she good looking, she had tremendous talent for music, especially singing. 
E. When she did start singing, she made a mark for herself in a short time.

Option C) DCEAB is the correct sequence of sentences to form a logical paragraph:

Sentence D introduces the protagonist, highlighting her appearance and musical talent.

Sentence C, then, reveals her reluctance to audition, which delayed her entry into the music industry. Sentences D and C can be linked, as D mentions her talent while C presents a contrasting statement.

Then, sentence E discusses the next part, indicating that she quickly made a mark for herself once she started singing.

Sentence A follows with her success story, highlighting that she received offers from music directors.

Sentence B concludes by stating that as a result of her achievements in music, she is now widely recognized as a popular singer.