The year before I graduated, several major Dallas banks came to campus and hired about a dozen finance majors. The year I graduated, because of the oil bust, not a single major bank hired a single graduate. To land a job at a major bank, I had to leave the region. I sent letters to the largest 100 commercial banks in the U.S. and was rejected by all of them. Looking back, having worked for some major companies with recruiting departments, it was probably difficult to respond to a resume that arrived in the mail to the bank's general address.
Major corporations get thousands of resumes for a variety of positions.
Don't just send a resume. She helped me get in touch with a well regarded officer in the commercial bank, and I called him up and worked out an interview. Once I had a contact on the inside, it was easy to get an interview set up with the right people. Major employers have entire departments dedicated to finding good people. When a candidate is willing to fly their own way out for an interview in exchange for just one-hour of their time, they jump at it.