I have a crush on someone right now, but that person is busy and hasn't replied to my messages.
Literal
Now unrequited-love [possessive-の] person [subject-が] exist [explanatory-のですが], unrequited-love [possessive-の] person [topic-は] now busy [and-て], email [subject-が] not-return-come.
片思い 'one-sided love, unrequited crush' — 片 'one-sided' + 思い 'feelings.' メールが返ってきません 'emails don't come back' uses ~てくる for the direction of the reply toward the speaker. The repetition of 片思いの人 is slightly awkward but authentic forum-post style.