Well, feeling sorry for you is a kind of caring, so the short answer is, "Yes. He still cares about you." BUT pity is NOT love and is not the basis for a full, healthy, loving relationship.
He broke up with you. You tried to patch it. Didn't work. You still love him, you say, but I wonder if it's really love for him that keeps you initiating contact. Seems to me it's more likely that it's your weakened sense of self-worth reaching out to him, seeking scraps of affirmation from him to help you feel better about yourself in the here and now ("Oh! He texted back! Oh! He's talking to me!" "I must be a person worthy of love!") in the long-shot hope he'll change his mind and get back with you.
You are trying not to fool yourself, and I commend you for it. You don't really want to, but you are correctly interpreting his silences and one-word texts as a message from him that he does NOT want either a romance with you or a close day-to-day friendship. He's sensitive enough to know you're vulnerable, so rather than getting nasty and dumping all over you, he's silent and hoping that you'll take the hint.
Maybe his passive gentleness endears him to you even more, but fight that inclination. I know you don't want to, but TAKE THE HINT ALREADY and leave him be.
Besides, you are love-worthy in your own right by virtue of your status as a human being, whether this particular guy loves you or not. You're demeaning yourself by groveling for his attention, and your insecurity-driven neediness probably strikes him as clingy and unattractive anyway. You're a WOMAN, for crying out loud! One of the most powerful forces of nature on this planet. Take a deep breath, stand up straight, square your shoulders, leave the nice guy's pity behind, and start moving through the world with a sense of strength. You'll be better for it, and so will your future romances.
OK, pep talk over. Though it might have sounded glib and rah-rah, I meant every word of it. YeeHah! <--- note authentic cowboy talk; I'm a transplanted city slicker to rural Lakeside CA and have a horse to prove it!