To save your reader time and to call attention to your strengths as a candidate, state your objective directly at the beginning of the letter. Example: I am seeking a position as a manager in your Data Center. In such a management position, I can use my master’s degree in information systems and my experience as a programmer/analyst to address business challenges in data processing. If you have been referred to a company by one of its employees, a career counselor, a professor, or someone else, mention that before stating your job objective.
How do you know for sure whether or not to use a closing? One good test is to ask yourself whether this email is more akin to an instant message/text or a business letter. If you're giving your teammate a quick update on an ongoing project, a formal closing might not be necessary; if you're throwing your hat in the ring for a promotion, it definitely is required. When all else fails, and you're still not sure, err on the side of caution and include it. You'll never go wrong by being too polite and respectful.