No harm trying, but you must know that there's fierce competiton. Almost every young upstart wants to get into banking and finance, especially after hearing things like record bonus from Goldman Sachs, and in spite of the uncertainty and relatively poor job security.

My advice: try for local banks first. Get into these (in order of pref): financial markets, corporate finance, institutional sales, then consumer banking. Then hop every 1 to 2 years.