When Does "Napoleon Dynamite" (2004) Take Place?
"Napoleon Dynamite" is a comedy film written by Jared Hess with Jerusha Hess [adapting "Peluca" (2002) by Jared Hess] that released June 11th, 2004. So when is "Napoleon Dynamite" set?
It takes place in the year:
We know this because the climax of the story involves a dance routine set to the song "Canned Heat" by Jamiroquai (Jay Kay, Sola Akingbola, Wallis Buchanan, Simon Katz, Derrick McKenzie, and Toby Smith), which released on May 24th, 1999 AD. So it must be after May of 1999 AD.

2004 AD
We know this because the climax of the story involves a dance routine set to the song "Canned Heat" by Jamiroquai (Jay Kay, Sola Akingbola, Wallis Buchanan, Simon Katz, Derrick McKenzie, and Toby Smith), which released on May 24th, 1999 AD. So it must be after May of 1999 AD.
More specifically, the opening of the movie includes a close-up of Napoleon Dynamite's student identification card which clearly says, "Preston High Preston, Idaho 2004-2005". HOWEVER, this is followed by the words "as Napoleon Dynamite" above "STUDENT NAME" since this is part of the opening credits and is therefore not part of the narrative's fictional world (diegesis). The co-writer and director has explained that this shot is intended to settle when it all takes place. In his words, "because they wanted to show that the film takes place now, there's a title where a hand pulls Napoleon's school ID out of a wallet and it says '2004' - that was like the big deal for Fox, hoping that would put to bed anyone’s question as to when it happened."
Although strictly just promotional (epitext), the film's poster also shows a flyer that reads "Pedro Sanchez for President Reach for the Stars 2004".