主句是 the child ... hasn't yet been found
lost a week ago 是分词做 child 的后置定语,可以认为是省略了 who was 的定语从句（the child who was lost a week ago）,因此要选C.
不选 D 的理由是在一个句子中,除非是并列关系,否则不能同时有两个谓语,选D的话就变成一个句子有 was lost 和 hasn't been found 两个谓语了.如果在 hasn't 前加一个 and 变成并列的关系,就应该选D,句子为：
The child was lost a week ago and hasn't yet been found.