、。
She kept on reading and didn't reply to me.
Literal
She [topic-は] book [object-を] kept-reading [then-て], me [to-に] reply [object-を] didn't-do.
読み続ける is a compound verb — 読む (read) + 続ける (continue). The て-form links this sustained action to its consequence. A good example of how Japanese compound verbs encode aspect that English handles with 'kept on.'