Should I include a career objective in my resume?

I am applying for a position in a field I left about 30 years ago. While there has been some changes in the field, I still have the basic skills set for this field. Since my recent experience does not speak directly to the position, I am re-doing my resume with a functional format. From the research I have done, it seems the jury is out as to whether HR’s would be looking for a career objective in the resume, or just to state it in my cover letter. (The preferred method of application for this position is via email).

Also, if applying via email, should a separate cover letter be attached, or incorporated into the message of the email?