#try either of these
/1/boards/[boardId]/cards?filter=closed&key=[your appKey]

It appears the syntax may have changed a bit. Neither of the above worked for me,
but this did: /1/boards/[boardId]/?cards=closed&key=[key]

https://trello.com/docs/api/board/index.html#get-1-boards-board-id-cards

https://api.trello.com/1/boards/{board}/cards?filter=closed&key={key}&token={token}
# ---------------------------------------------------^^^^^^

https://api.trello.com/1/boards/{board}/cards?filter=all&key={key}&token={token}
# ---------------------------------------------------^^^