Garden State (2004)
This is the movie with Scrubs actor Zach Braff and now-Oscar winner Natalie Portman that helped make the Shins a pretty big deal.
In Good Company (2004)
It didn't make as big of a cultural splash as Garden State, despite having a similar pairing of young-TV-actor-turning-to-film and up-and-coming-actress (Topher Grace—Eric from That 70's Show—and Scarlett Johansson), but it features just as many Shins songs, which makes it plenty worth checking out.
Gilmore Girls, Season 4, Episode 17 (2004)
The show full of rapid-fire quips and ever-changing romances had the Shins on to perform their song "Know Your Onion" in a club that main character, Rory, goes to. Read about the episode to see how some of the Shins sound might match the feel of this TV drama.