There has been no finding by any authorized body, judicial or legislative that Barack Obama failed to qualfy under Article 20. He stopped being President-Elect when he took the Oath of Office on Inauguration Day.
A federal judge ruled on this in 2009 in a lawsuit that went all the way to the Supreme Court of the United States:
Barnett v Obama, US District Court Judge David O. Carter: “There may very well be a legitimate role for the judiciary to interpret whether the natural born citizen requirement has been satisfied in the case of a presidential candidate who has not already won the election and taken office. However, on the day that President Obama took the presidential oath and was sworn in, he became President of the United States. Any removal of him from the presidency must be accomplished through the Constitution’s mechanisms for the removal of a President, either through impeachment or the succession process set forth in the Twenty-Fifth Amendment. Plaintiffs attempt to subvert this grant of power to Congress by convincing the Court that it should disregard the constitutional procedures in place for the removal of a sitting president. The process for removal of a sitting president—REMOVAL FOR ANY REASON—is within the province of Congress, not the courts.”U.S. District Court for the Central District of California, October 29, 2009
http://ia600204.us.archive.org/1/items/gov.uscourts.cacd.435591/gov.uscourts.cacd.435591.89.0.pdf
The Supreme Court ruled in Fairchild v. Hughes that all citizens have a right to a government that is administered according to law. The seating of an ineligible president does not conform to the law (or the Constitution), thus such a person is not technically a "sitting" president. Under Art. III, it is within the judicial power to resolve controversies that arise under the Constitution. This is not a power delegated to Congress. There's no reason that the courts cannot enforce Art. II and the 20th Amendment in order to ensure that all citizens have a government that is run according to law.
I just proved that he failed to qualify under the Twentieth Amendment, Section Three. It is his burden to qualify in order to meet the Constitutional requirements for holding the office of President. His "failure to qualify" still stands as is. If Congress refused to do its job under the Twentieth Amendment, Section Three, that doesn't equate to him "qualifying" at all.
You are correct about him being "President-Elect" until election day. From that day on he became a usurper, not a legal President.