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I have the ciphertext and an encrypting program (with the key hardcoded in). How would I go about finding the key? Surely the availability of the encryptor must open up possibilities beyond brute-forcing it.

A: 

Yes knowing the algorithm may help in decoding the cypher text, but only if there is a flaw in the algorithm that may be exploited. (the good news is Playfair has some flaws that can be exploited)

Here are a few good starting points to read.

  1. Wikipedia (read it all - particularly Cryptanalysis)
  2. Basic Cryptanalysis (look at chapter 7)

The second one is not what I would call a light read, but interesting if you're into cyphers.

Chris Mc