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One would think that with enough computing power, you could decipher the cipher.

The problem is that it's not a cipher, it's a code. A cipher is a substitution - often with a very complex substitution algorithm (e.g. the famous "Enigma" machine of WWII). But there is still an underlying pattern, and computers can attack it to find that patter. It's aided by the fact the "unencoded" message follows the rules of language (most common letter in English is "e", etc.).

But a true code uses one word or phrase to refer to an entirely different item, and there doesn't have to be a logical relationship or anything else that can be attacked by a computer. If you have a big enough sample you can sometimes work out the code relationships, though it's often just a probability rather than an assured translation. The famous example here is the deduction that "AF" meant "Midway" in the Japanese code just before the battle of Midway, deduced because the pilot who transmitted a message about "AF" was flying near Midway at the time. But AF could have meant anything, and all the computer analysis can tell you is that some transmitted characters (in this case, in "coded" Japanese) become "AF" when "decoded" (that's the cipher part).

A book code or document code needs the translation book to let you know that 793 214 refers to "north", and not "apple." The most a computer can do for you is to let you know if a candidate book or document might be the basis of the code by whether the resulting 'clear language' message makes sense. If you try Genesis as the basis of the book code (as apparently someone did with the Declaration of Independence) and it starts translating into something that looks like meaningful sentences or data, it might be the right book. However, even that is version dependent.

One would think that with enough computing power, you could decipher the cipher.

No, not if its a book cipher. A book cipher uses numbers like page number, line number and character number to encode text. For example 4,15,37 could mean 4th page, 15th line and 37th character. With codes like this the book in question becomes the key to solving the cipher, not unlike what cryptanalysts call a "one time pad". Without the book in question, and the specific edition of the book in question at that, you are pretty much out of luck. It says on Wikipedia that one of the three documents was decoded using a specific printed edition of the Declaration of Independence. If one were to take this seriously you'd start by checking it against old out-of-print books that were around when the cipher was written (might be a job for Google Books!) Of course there is the very large probability that this is all an old hoax.