Well I'll give you a few pointers, rather than sympathy or reliance, more constructive things to work on cause maybe that'd help more?
Now by the sounds of it you want to make deep, non-surface level friends, and doing so is actually rather straightforward I find, but being straightforward doesn't mean it's easy. So lets talk about some of the things you can do.
1. Show interest in someone: Not romantic interest mind you, I just mean interest. One of the things people really like doing is talking about themselves, if you want to create a strong friendship you have to show you are interested in hearing that. This interest should be genuine though, but you may find someone you were originally not interested in, becomes interesting once you know a little bit more about them! So basically ask questions, how was your day, what are you doing? Is everything ok? These questions should be all about them, you shouldn't go "How was your day?" "IT was good I did X" "OH that reminds me of when I did X!" No, you shouldn't be waiting for your turn to speak about yourself, you should just listen, ask questions and take notes. That's the first step of getting someone a little closer to you. (Keep in mind if they ask YOU a question then the roles are reversed and you can talk about yourself, but if they start talking about themselves again go back to listening, this is not permanent and is just at the start of the relationship).
2. Becoming vulnerable: Deep relationships are built at the core on a sense of mutual vulnerability and trust. Vulnerability and trust is putting yourself in a situation where the other person could harm you, and doing so can be frightening and potentially dangerous. One of the tricks to maintaining a good level of healthy vulnerability and trust is to keep at whatever pace they're going AND that you're comfortable with. What this means is as you ask questions about them, they'll eventually reveal more and more facets of their life, they'll start revealing things about them that they consider personal, and sometimes even secret. You reveal at their pace, when they say something they consider not public but also not too personal, you should then reveal only on that level, not your deepest darkest secret right away. Relationships take time to build, sometimes in months, sometimes in years, a relationship that blossoms in only a week is usually a very unstable one full of high peaks and very low ebs. Learning not to reveal too much too quickly or too little too slowly, is important, moving at their pace. And when they reveal something secret, its helpful to know that they know something about you too.
3. Helping and supporting: One of the important things about a relationship is being helping, when your friend is down you should be there to help them (and ideally the same would be said in your situation). But again you follow 1. and 2., you don't start off a relationship by skipping to 3, sometimes when your friend is feeling down they may not want to talk, you haven't created that level of trust yet and, in those situations you should just say "I'm here if you need me", remember, relationships require patience (I should also mention even deep friends may not want to talk all the time, people handle problems in different ways!). Conversely you shouldn't start a relationship by asking for help yourself, that's the origin of an unhealthy relationship! You can ask help from people at any time but if you want to create a strong relationship, you need to start at the surface, and you need to start with "I'm your friend" not "I want you to be my therapist". But it is at those times when people are at their worst, after a mutual trust has been gained, that the strongest of bonds of form.
There's more to it but the rest you kinda have to figure out on your own, making a strong relationship requires work. But eventually the "work" won't feel like work, and you'll have a friend you can talk to with just about anything.