I'm truly not saying the fact that you don't have any wonderful friends is your fault, so please don't take this that way. And I'm not saying you aren't a good friend as it is, because I simply don't know that. But the thing is, if you try to become the sort of friend you described for someone else -- and I mean really go out of your way to try to personify exactly what you've described, even if your good-friendness isn't being reciprocated at first -- it's not unlikely that they'll eventually respond the same way. It won't be immediate, and it may not be easy, but it will help. This probably sounds quite intuitive, and you probably already know about this. I'm just suggesting that you do it much more consciously.Additionally, while finding new friends might be the best thing to do, it may not be very possible -- perhaps your community doesn't have a lot of opportunities for that kind of thing. In that case, I recommend confronting your old friends about their back-turning. 'Confronting' may be the wrong word; it should be done with a very polite, kind, 'I want to repair our friendship' sort of way. I don't know what happened with them, but if you can possibly forgive them, it might be in everyone's best interest to do so. However, being standoffish or unfriendly in the aftermath of their betrayal -- while perfectly understandable -- may be making things worse.
The thing is, just because friends experience a falling-out from time to time -- even a really major, major falling out -- doesn't mean that it's not a 'true' friendship. It just means that the friendship needs some work. But if you're so upset about your social situation, no matter how hard you try to hide it, people will know -- or sense -- that you're unhappy, and that won't make your friendship-building prospects very good.