Former “American Idol” runner-up Clay Aiken officially filed Thursday to run for Congress in North Carolina, saying that he wants to help end the gridlock in Washington and that no single political party has all the answers. The performer, a Democrat, turned in his paperwork at the State Board of Elections to seek the 2nd District seat currently held by Republican Renee Ellmers. Aiken, who lives in the Raleigh-Durham area, announced his bid three weeks ago and must first try to win the Democratic primary in less than 10 weeks. …