The resume that you describe, namely a brief overview that highlights your accomplishments, is actually called a cover letter. A cover letter is a good idea, but it is not a substitute for a resume. A good cover letter should induce a screener to read your resume, and a good resume should induce a screener to call you. While it is possible that a vague and general cover letter can generate some interest, the odds are that it will not. And in the job pursuit process, you want as many odds in your favor as possible.
You should go back to your resume and review it as if you were a screener. It should be clear and readable, and it should include a statement of your objectives, followed by jobs, titles, dates of employment, and main responsibilities. It should be no longer than two pages, and there should be no typographical errors. Be sure to include key words that fit the position you seek. There are plenty of books that provide samples of excellent resumes, and you should have no trouble tailoring a resume to fit your background.
A resume that leaves out dates and other relevant information can easily cause an applicant to be left out, too.
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