Because her parents divorced, the girl had almost no contact with her father.
Literal
Parents [subject-が] divorced [reason-ため], that girl [topic-は] almost father [with-との] contact [subject-が] didn't-exist.
~ため (because/due to) marks the reason clause more formally than ~から or ~ので. ほとんど + negative = 'almost none.' 接触 (contact) is a formal word. A sentence about the consequences of divorce on parent-child relationships.