Unqualified means (1) "not having proper or required qualifications" (such as achievements, records, background) and (2) "not restricted, modified, or limited": "Until he passes the bar examination, he is unqualified to practice law in this state. When he does so, he will have my legal business and my unqualified confidence." Disqualified means "deprived of rights and privileges," "rendered unfit or declared ineligible": "After his conviction, he was disqualified from holding a public position."
Dictionary of problem words and expressions. Harry Shaw. 1975.