motivation

Is it possible to be motivated and un-motivated at the same time?
I am positive that I want to be in California this summer. I think about it all the time. I am dreaming big. I have plans. Or as close to plans as I can have. I heard recently that DC4C called their last album "Plans" because it was the punchline to a joke, "How do you make God laugh?"
I think it's the little steps that I have trouble with. I feel as though those should come easily, given my level of overall motivation. I've requested transcripts, polished my resume, tracked down a handful of internships I'm interested in, and asked for recommendations.
Ok, so maybe I've actually done a lot. What is really challenging me are the cover letters and a professional statement I have to write. In the past, they've been an afterthought. Now, I realize that they're a great chance to express myself to the company. I'm a good writer. I just owned a letter writing assignment that most of my class bombed. I think I'm having trouble with it because it means so much. It's all I can do not to write "Dear Mr. Executive, I'm bored with Boston and I miss my best friend. Please hire me so I can experience some adventure this summer and build my resume." How can I balance desperate with motivated, and bored with qualified? What can I bring to a company besides drive?
Maybe I should just write it raw and then edit after. That's not my usual working style, but maybe it will work. I'm hoping writing this all out here helps in some way.
Gah, it's just a cover letter! Maybe I'll just work at a Jamba Juice and live on someone's couch this summer. That wouldn't be horrible.