The first full trailer for the upcoming David Fincher-directed remake of The Girl with the Dragon Tattoo has been released today. You can watch the trailer below this article.

Running nearly four minutes, the new trailer mixes the extravagant visuals (a Fincher specialty) we first glimpsed in the teaser trailer that was “leaked” several months ago with a stronger emphasis on the film’s story and the character of Lisbeth Salander, played in the remake by Rooney Mara (The Social Network). The central mystery of the story is laid out nicely without spoiling any important information.

In recent months David Fincher‘s upcoming remake of The Girl with the Dragon Tattoo has been an enigmatic figure in the film world, from the release of a controversial poster that featured star Daniel Craig (playing disgraced journalist Mikael Blomkvist) with his arm around a topless Rooney Mara (assuming the key role of haunted hacker Lisbeth Salander from Noomi Rapace) to the leaking of a very brief teaser trailer that presented an onslaught of images set to a propulsive cover of Led Zeppelin’s “Immigrant Song” recorded by Nine Inch Nails frontman Trent Reznor and Karen O of the Yeah Yeah Yeahs.

Late last year it was announced that Reznor would be reteaming with English musician (and producer of four NIN albums, among others) Atticus Ross, who he had successfully collaborated with on the score for Fincher’s critically-acclaimed box office hit The Social Network, to provide the score for the Girl with the Dragon Tattoo remake. Now, Sony Pictures has released a 7-minute sample of Reznor and Ross’ score at the film’s official website; you can listen to it below this article in the embedded YouTube video.

The David Fincher-directed film The Social Network, which stars Jesse Eisenberg as Facebook creator Mark Zuckerberg, is doing great this awards season, and there’s a good chance the film will take the Best Picture Oscar this year.

Right now there’s some great deals on the DVD and Blu-ray, as well as the film’s soundtrack, which won Best Score at this year’s Golden Globes.

— The Social Network Soundtrack, by Trent Reznor and Atticus Ross, on MP3 for only $5.00 and on CD for only for $9.99.

— The Social Network 2-Disc Collector’s Edition on Blu-ray for only $16.99 (that’s 51% off the list price of $34.95) and DVD for only $12.99 (that’s 55% off the list price of $28.96).

— Video On Demand: $14.99 to purchase; the 24-hour rental will be $3.99 (rental for this film will be available starting February 2, 2011).

The MP3 deal of the day over at Amazon today is The Social Network Soundtrack by Trent Reznor and Atticus Ross for only $2.99.

The MP3 version of the album, which contains 19 tracks, is available exclusively through Amazon until its wide release on September 30. The CD version is available for pre-order now for $7.99 and will be released on October 15.

Usually the MP3 deal lasts for 24 hours, but this one might be extended for 48 hours. If you’re a fan of Trent Reznor and Nine Inch Nails, you should definitely get in on this deal right away.

Make no mistake about it: when we first heard that Fight Club, Se7en, and The Curious Case of Benjamin Button director David Fincher was making a movie about Facebook of all things, we scratched our heads. At that time, however, many of us probably had visions of a live-action Tron-esq Facebook world with farm animals and Mafioso running about, upwards thumbs flying through the skies, and everyone poking the ever-loving hell out of each other 24-hours a day.

That of course is not the case at all. Fincher’s movie, called The Social Network, is actually based on the Ben Mizrich book, The Accidental Billionaires: The Founding of Facebook, A Tale of Sex, Money, Genius, and Betrayal. And to add to what’s sure to be a compelling tale, it’s now been officially announced that Trent Reznor, frontman of industrial rock band Nine Inch Nails, will be handling the film’s musical score along with composer Atticus Ross.

Click over to read Reznor’s announcement and to check out the first teaser trailer for The Social Network, if you’ve yet to see it, of course.