Next time something is your #1 choice, or even your number #42 choice, you need to be a little more proactive. Polite persistence is the only way you're going to get what you want when you're dealing with someone that's got plenty to do and couldn't care less about you as an individual.
It's not a typical job application. It's a very formal bidding process, where internships are posted to the university's computer system, and students can bid for interviews through the system. Students have a limited number of bids they can use, and bidding on an internship does not guarantee you an interview. Your resume, transcripts, cover letter, writing sample, etc., are all transmitted to the employer electronically. The employer does not post contact information. The only avenue of contact a student has with a potential employer is through the system, and even then you are limited to being able to submit a bid which includes any documents the employer has requested, and a note, if you wish to leave one. Beyond that, there is typically no contact. Now, I have an email address, of course, because I was emailed and asked to email more info. I sent that email (four hours too late) and followed up the next morning with an email asking if that sufficed and if there was anything else I could provide, etc., but got no response. There's little more I can do, and that is by design. The employers do not want to be rushed by 1000 law students all jockeying to make the best impression to snag the summer internship.