Hold on a minute, am I getting this straight.. You want a sense social belonging... in league of legends of all places?

You surely know that game is renowned for its genuinely toxic fanbase, right? Doesn't matter how popular it is, it's designed to be competitive and hostile. Try a co operative MMORPG, maybe something like guildwars. Honestly it sounds like you're just starved of a social life, have you tried volunteering somewhere? Plenty of places will take anyone who is willing to give their time, you'll meet people and it might even help you sort your life out in other ways. At worst, you'll have done something positive with your time.