The Board shall hear and determine appeals from any decision of the Secretary or any position or unit within the Department subject to judicial review under the Administrative Procedure Act or any other provision of law. The Board also shall hear and determine any appeal from action or failure to act of any position or unit within the Department for which the Secretary, by rule or regulation, provides for review by the Board. A Board member may not participate in any determination or vote in any proceeding as to which he has, directly or indirectly, a private interest.