Congress certified the vote count,not his eligibility. For that they were relying on the Secretaries of State of the several states, who in turn were relying on the DNC who in those states where it was required, such as Hawai`i, certified Barry as eligible.
I meant to add a
link to a copy of the document (it's the third and last document in the file), wherein Nancy Pelosi and Alice Germond certified to the state of Hawai`i, Office of Elections, that BHO is "legally qualified to serve under the provisions of the United States Constitution".