It may surprise you to hear this but, these days, you are not alone. Many of us feel disconnected. In past times, people were less mobile and often tended to stay in the same town/city/neighborhood for their entire lives---as did their extended families.
You said that you moved to a new state for financial reasons. Are you living in a transient area? If so, in such areas, people (generally speaking) don't want to put in the effort to make connections. Their thinking is that people will move anyway, so why bother.
Yet, paradoxically, if you are in an area where people still tend to be rooted for their entire lives, it can be hard to make connections. In tight-knit communities (again, generally speaking), people are slow to warm up to newcomers. If you are in such a community, don't give up.
You mention being depressed. Not to be trite or dismissive, I'll pass along this advice --- always put a smile on your face when you interact with others. I know that some days it will be difficult for you to do so but it is worth it. I have found that on days when I feel down, putting a smile on my face and chatting with someone is uplifting.
It sounds like you have really made an effort to connect with others. I suggest that you don't give up. Maybe you won't make friends but you will have acquaintances. It's sad when you think you've made a lasting connection, only to have that person exit your life---believe me, I know. Yet, there is another way of looking at it --- people come into your life for a season and a reason. Perhaps, they were there when you were really feeling down and their presence helped. When they make themselves scarce, hold on to the positive memories of that time.
Are you in an over 55 community? If not, consider moving into one, if possible. People who move into such communities---even if they are shy---often talk about the connections the've made. These communities have activities you can participate in. Some have common dining rooms where you can have your meals. As people get to know you, they tend to look out for you---and expect the same from you. That doesn't mean that you have to watch them constantly. Rather, it means that if you need help, it is there.
Have you tried using the web? Do you have a hobby or any interests? If so, search the web for chat rooms devoted to your hobby or interests. The advantage is that you are there under a screen-name and there is no pressure to reveal your name or where you live. As you participate in the chat rooms/forums, you start to get a feel for the other participants. If you make a connection with someone and it turns out that they live not too far from you, you can arrange to meet up in a very public location.
In conclusion, I will say this -- don't give up. When you go outside, put a smile on your face. If you make a transaction with a sales clerk who is friendly and there isn't a long line behind you, make some small talk. It's not the same as having a friend but over time, if you shop at the same store, you will get remembered. Such interactions help boost your spirits.
Recently, I went to get my haircut. As I entered, I did what I always do, smile at the receptionist and say hello. She knows who cuts my hair and will tell me to go back and talk to my stylist. One day, while I was getting my hair cut, the receptionist went to my stylist to ask a question. The receptionist looked at me and said to my stylist "Every time she comes in she, always has a smile on her face and that's so nice". That told me that most people don't even smile or say something nice. It also told me that a smile goes a long way.
Best of luck to you. And yet once again, don't give up trying to make connections!