It really is all about who you know. for Better or for worse. (I'm not really a fan of Nepotism, but that's the way the world works)
I had the same dream, but i gave up on it
Due to practical concerns such as finding a job to pay the bills. I must have applied a 40-50 times to virtually every airline in the US, plus some international ones at LAX
and only American Eagle responded with a group interview (didn't make it to their second round unfortunately).
Internships really help, though that's more of a student thing, and not always feasable but most importantly NETWORKING; that was my disadvantage; graduating college, i wasn't able to get an internship and had virtually no contacts, plus I'm a shy person by nature. If you can find events to go to, job fairs, trade shows, what not for airlines, try to make as many connections as you can, even if you don't talk about employment day one, just chat and make connections, and BE
PERSISTENT as they say. Its a bad time for airlines, and unfortunately all i saw was part-time jobs that paid VERY bad, but if you really want it, its a start.
Me? I ended up going into Airport Operations, pay is much better starting out than what an airline pays, but i still some times catch myself wanting to work for an airline...
Keep trying, its very frustrating, i know, but if you really want it you'll get something.