The Moriarty Sentience Problem - A.K.A. Why isn't the Enterprise computer considered sentient?

In Elementary, Dear Data, Geordi instructs the computer to create an opponent to intellectually best Data. The conceit of the episode is that the computer does just that, and creates a sentient hologram that is aware of his nature and the 24th century world. This accidental creation is deemed alive, and sentient.

Here is my problem - Moriarty is a simulation, a program, created by the computer, using only information it had; it is run on the computer, making decisions as best as the computer can. Moriarty is the computer of the Enterprise. Why is Moriarty, an application, considered sentient, and the computer from which it was created and on which it runs, not?

Please address in your answers the creative problem solving demonstrated by the computer that created this whole problem. Gerodi didn't ask the computer to run "sentience simulator 257-beta", he asked the computer for someone who could beat data. The computer creatively made sentient life. How can the created be sentient, and not the creator? This isn't the Enterprise evolving, its the Enterprise creating.