OK. I need real help with shy guy.

this guy sounds severely shy and is distancing himself to protect him self from making a mistake in front of you

for someone so shy you ought to try risking the break in his personal barrier.
next time he sits away from you walk over to him sit down and tell him that you wish he'd open up and trust you. tell him you won't hurt you (the breakup may traumatize him unless you simply stay friends)

be goodnatured sincere and kind.

he wouldn't go into the same cafe as you if he didn't like you
he wouldn't look at you if he didn't like you...why would he pity you?

shy guy here lol, if I was in the position and I did like you, id want you to make the first move and maybe even the second move. maybe you should just ask him if he wants to share a table. and don't take the no eye contact thing personally, its just hard to look pretty girls in the eye for some reason. Try getting his number and texting him for a while, that gives us time to think about what to say and such. or hell maybe he doesn't have any interest at all, that's why you should just be straight up with him.

I was shy once, but I join the military so I can only give you what I have now:

He interested in you, likes you, and wants to ask you out but you not giving any effort IE going to sit next to him, trying to hold his hand, these are items that will boost is confidence, hell watch some Anime, the japanese girls almost ALWAYS go for the guy, drop plenty of hints and when hints fail go to the "I love you". It's not hard, but if your new to the field of girl and guy flirting/looking for a mate - you might be less attracted to the idea of following through with your true feelings. Also...

DON'T EXPECT HIM TO ASK YOU OUT. You're a teenager, maybe going into the age version (not maturity) of woman hood - go ahead and take your first real step and tell him you like him, love him, stop waiting for signs, that's very old tactics. Here something to thing about;

"Pardon me ma'am, your quiet beautiful in that dress." catch line many males use, now turn it around in your head and walk up to the man or if you feel like calling him a boy, do so.
"Hey, what you up to?" there you go, first start.

He's only saying, "hi, thanks, ok", make him have to give you an answer, BUT DONT BE RUDE OR MAKE IT SOUND NASTY BECAUSE HE'LL GET THE HELL OUT OF THERE. "It's been raining alot, wonder when it'll clear up" sure lame and cheesy but he'll be inclined to give you an answer him "yeah" you "think it'll clear up sometime soon? I'd like to go to the beach, do you swim?" him "sure" even if he's shy, starting a conversation, open or end what you say so he can answer with more than 1 word. He's no going to talk much, so do the talking, take a few steps, go out on a limb.

You will have to give him a hint like aaron28 suggested or you have to directly tell him that you think he is cute, attractive, or handsome, etc. Because shy guys never really build up the courage to ask a girl out or tell the girl how they really feel because they are really afraid of rejection from the other girl. You would have to do something that would make him know that he has a less chance of being rejected.

Being a shy guy myself he could very well be interested in you, from what your describing. Perhaps he just needs a boost of confidence and gentle nudge from you. Next time you talk to him you might give him the opening like "I really want to see this movie friday, but I have nobody to go with"

Make it known to him that you're interested, but don't bother pestering and bugging him about it. If he likes you, he'll eventually make the effort, if not than move on girl!