Using humans as components to build a computer?
Actually, until the 1950s the word computer was used to refer to a human who did arithmetic calculations.  One (or more) of Richard Feynman's (many) autobiographies contains anecdotes about his time on the Manhattan project, where he ran the group of human computers. For arranging a group of humans to perform a complex computation they wouldn't start with discrete logic components, but rather have each human perform multiple arithmetic operations and then coordinate their results (along with some error checking.)  How to organize these kinds of large computations may be covered in numerical methods books from the 1940s or early 1950s.

The first version of the Logic Theorist by Newell, Simon and Shaw was simulated using humans in 1956 (less expensive than computer time).  They later won a Turing Award for basic contributions to AI, the psychology of human cognition and list processing (the Logic Theorist may have been the first program to use linked-lists to represent data structures.)  And the experience influenced Simon's later ideas on emergent behavior (see his Sciences of the Artificial.)

As pointed out in the comments and other answers, there is now an emerging discipline of Human-Based Computation, where various incentives are used to get humans to do parts of a larger calculation, where those parts make good use of human problem solving or pattern recognition.  One example of this is reCaptcha, where users need to enter two words to prove that they are not a bot, one a distorted image that is used for the actual "proof" and the second an actual word from a scanned book, which is used to produce a digitized version of the book.  Another example is the Amazon Mechanical Turk where a business can outsource "microtasks" to human workers for small sums of money.  The mechanical turk has been used, for example, to collect annotations on 250,000 images for image processing research.  The key seems to be breaking the problem down into a pile of independent work items, with significant amounts of redundancy used to reduce errors.  (E.g., you assign the same work item to 2 different humans, and then if they provide conflicting answers you assign the work item to a third human to resolve the difference.)