Zeraph

I'm trying to decide what to say in a cover letter for a job I don't have any direct qualifications for. Basically I got my bachelor's in Psych and am not going toward that career path. All my work experience is in education, another line I don't want to follow. So when posting a cover letter, what the heck should I say (besides the obvious "hi I'm X and applying for X thanks sincerely..."

I'm thinking something that say's nothing but conveys my professionalism and intelligence. Or would that just seem empty? Any tips? thoughts? Maybe I just shouldn't send one at all if I have nothing important to say and just send my resume.