Well my goal is to get a Financial Internship, but its seems pretty hard as my career services doesn't really get any recruits from investment banks or PE firms. I've tried sending my resume out all over the place but no one really responded, hopefully I can get one before I graduate but its unlikely.
Have you tried sifting through your alumni database? I assume you're at a non-target based on your difficulty in getting a look. Does your school have a business college and is there a separate database for internships there? I would go through your alumni database and find people that are in the field you would like to get into and network with them. If that fails, I'd also start cold calling firms; you might have to accept an unpaid internship (but only consider this if it's related to the area of finance you want). Join some investment club or finance club at your school to network and learn about the field.
If you're in college, don't you have the freedom to change your major to finance or economics? While you're in college is a great time to think about what you really want to do and switch; it's far easier. Once you graduate and have "Chemical Engineering" on your resume and a bunch of engineering internships and jobs, anyone looking at your resume will peg you as an engineer.