Obama and Biden got the majority of the electoral votes, and I'd be willing to point you to any number of sources that agree with that. They won the election, they were sworn in in January, and the 20th Amendment no longer applies. Now if for any reason, any reason at all, Obama is removed from office then Biden is President per the 25th Amendment.
If Obama was not eligible then he is not the president, was not the president, has never been the president, and cannot be removed from office because he does not hold the office. Biden was elected vice-President, not President. Biden would only act as President until congress voted for a new President.