。
She had nothing to be ashamed of.
Literal
She [topic-は] conscience [at-に] be-ashamed thing [subject-が] did-not-exist.
良心にはじる (りょうしんにはじる) means 'to be ashamed before one's conscience.' ところがない ('there is no aspect/point where') negates it — she had no reason for shame. はじる (恥じる, 'to feel shame') is somewhat literary; the expression as a whole is formal and written.