No sooner he (start) to play than one string on the violin (break).

Правильный вариант предложения:

No sooner he had started to play than one string on the violin broke.

Данное предложение можно перефразировать:

No sooner had he started to play than one string on the violin broke.

The Past Perfect is used with the conjunctions \"No sooner ... than\" according to the following schema:

No sooner + Past Perfect + than + Past Indefinite.