What symptoms of a hopeless lover does Romeo exhibit?

One of the best places to find answers to this question is the conversation between Benvolio and Lord Montague in the first scene of the play. Benvolio claims to have seen Romeo "early walking" alone in a sycamore grove, but when Benvolio—Romeo's good friend and relative—tried to approach him, Romeo "stole into the covert of the wood" (1.1.113, 1.1.115). In other words, Romeo has taken to wanting to be by himself, out and alone at night, and he's lost all desire to speak to even those people who love him.
Lord Montague tells Benvolio that Romeo has been seen there a lot lately, "With tears augmenting the fresh morning's dew, / Adding to clouds more clouds with his deep sighs" (1.1.122-123). So, Romeo has been crying and sighing a great deal recently as well, going to the same place to wander in darkness and be alone. Then, when the sun begins to rise, Romeo will finally return home, "And private in his chamber pens himself, / Shuts up his windows, locks fair daylight out, / And makes himself an artificial night" (1.1.128-130). Thus, Romeo is not only crying and dejected all the time but he also he wants to be in the dark, never in the light. He returns home to avoid the sun and then makes his room as dark as possible during the day. This physical darkness echoes the figurative darkness, or the lowness, of his spirits. Further, Romeo will not tell his father the cause of his distress either.