I'm so sorry for your suffering and loneliness.

You aren't hopeless or alone.
I'm a natural introvert and hermit, so I don't have any
great suggestions.
I'm not sure whether you are looking for advice on bettering/deepening your connections with people or just going out socializing and making new friends?
Deepening your connections (I would think) would be unique to the person/individual. Therefore, the approach could differ.
If you are looking to get out and socialize more, I can suggest what other people suggested for me when a posted a thread entitled "Breaking out of my shell"...
- Volunteering at the library or animal/homeless shelter
- Meetup.com (site to help you find and meet up with people local to you with common interests)
- Join a book club (I'm a bookworm)
- Get a part-time job that interacts with the public
- Pick up a new hobby (Yoga, knitting, rock climbing, creative writting course, etc.)
Like I said, kind of lame after reading your post, but I just wanted to write you something. Your pain is obvious in your words and they hurt my heart. You aren't alone.

Please, keep posting.