。
She asked me whether there was a problem.
Literal
She [topic-は] some problem [subject-が] exists [question-か] [quotative-と] me [to-に] asked.
~かと + a verb of asking is the standard frame for embedding a yes/no question inside reported speech: ある ('exists') becomes あるか ('does it exist?') becomes あるかと尋ねた ('asked whether it exists'). Note the か here is the question particle, not the alternative-listing か. 何か does double duty as an indefinite — 'some problem' rather than the questioning 'what problem' — a common use of 何 + か outside direct questions.