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Mailed around 400. No response at all.

I included cover letter, resume, transcript and writing sample. Now what can I do (or what should I write in cover letter) to maximize the chance to get interviews?

Thanks!

How long has it been? If it's been over a month, send follow-ups. I've gotten a couple of skype interview requests from doing that. I mailed about 200 apps, so you may get a better return.

Just say something like:

I am writing to check on the status of my recent application to your summer associate program. I know you are busy with the hiring process, and I appreciate your time and attention. Please let me know if I may provide any further information.