、。
Since she didn't have a car, she stayed home.
Literal
She [topic-は] car [subject-が] did-not-exist [because-ので], home [at-に] was.
~ので (because) gives the reason — no car — for staying home. なかった (past negative of ある) means the car didn't exist/wasn't available. 家にいました (was at home) uses the polite past of いる. ~ので is softer and more objective than ~から for giving reasons, appropriate for a neutral explanation of circumstances.