[Spoilers below, including in the non-hidden parts]
The computer never answered the question. Instead it threw a question back at them that one of the PhD's had asked almost rhetorically earlier in the film: "How come we're asking a machine that's never felt a thing, never felt love, and pain, hunger, never felt faith or a gut instinct... why are we asking it a question about God? You know, honestly, why are we asking?"
There were no human responses to this answer; the film ends immediately.
Prior to this resolution, at each earlier attempt the computer would consider the question for several hours and then shut itself down, committing suicide in effect, rather than give an answer or allow humans to examine computer memory to deduce what its thoughts were on the question. The computer's responses during this time seemed a riff on Asimov's "The Evitable Conflict" where the Machines politely refuse to answer questions about their actions with "The matter admits of no explanation."
"Do you remember the Machine's own statement when you presented the problem to him? It was: 'The matter admits of no explanation.' The Machine did not say there was no explanation, or that it could determine no explanation. It simply was not going to admit any explanation. In other words, it would be harmful to humanity to have the explanation known, and that's why we can only guess - and keep on guessing."
Answering the question directly would somehow be harmful to humanity, so the computer chose ultimately not to answer. This result was deeply foreshadowed earlier in the film, and given how poorly the question was formulated, inevitable.