step one is don't feel bad. it really is a numbers game. some of the companies you're applying to don't actually want to hire anyone for the position right now. some of them are desperate to get anyone with a pulse yesterday. it's all about timing, but you don't usually have a way of knowing when the time is right.
just keep rolling the dice; you'll get a bite eventually. I got an internship that lead to my first full-time job when I had a 2.4 GPA. I just happened to have experience with relevant tech that was rare in the area and they gave me a shot.
So while what you say is true, my potential network is necessarily limited. Working in retail, I still met plenty of people who wouldn't even let me assist them because of my race. I think this may go beyond personal qualities.