The first answer was correct: David Soul was Number One for four weeks from January 15th 1977.
Julie Covington became Number One on February 12th 1977 and was followed by Leo Sayer with "When I need You." info: Answers.com
Incidentally a British act was number one in US at same time: Mannfred Mann with "Blinded By The Light."
Don't Give Up On Us is right. Don't Cry For Me Argentina was number one for the week ending 12 Feb, i.e. the week beginning 6 Feb - so too late for 2 Feb in any case.