The Seattle-based e-commerce giant is testing a service, dubbed “Amazon Unbox Video,” that will allow U.S. customers to rent or buy digital videos, including movies, television shows, news shows and sporting events, according to a draft of Unbox’s terms of service captured by a Business 2.0 contributor and published on the publication’s B2Day blog Saturday.

Meanwhile, a screenshot of the service’s main page that was posted on the Web suggests Amazon will charge $1.99 for most TV episodes. Another page showing science fiction and fantasy films lists “The Matrix” at $9.98 and “Alien Vs. Predator” at $10.97, and lets shoppers narrow their film search by category, director and studio.

Web developer Alan Taylor, a former Amazon employee who posted the screenshots on his Kokogiak blog Thursday, said he found the Web pages after discovering a side door into the service that Amazon left open inadvertently.

An Amazon spokesman declined to comment on the authenticity of the documents or details of the video-download service. In a bid to find new growth, the company has in recent quarters spent heavily on technology, Web content and software development for competitive initiatives including download services for digital books, movies and music. The spending has pressured Amazon’s profit margins and weighed on its financial outlook and stock price.

Amazon shares recently fell 87 cents, or 3%, to $28.25. The stock has rebounded from hitting a three-year low of $25.76 on Aug. 11.

Judging from the details of the video service posted online, “it appears Amazon is close to this long-awaited service,” Bear Stearns analyst Robert Peck wrote in a note to clients Monday. “This service should boost margins if it gains traction and may ultimately replace any idea of a Netflix type business,” referring to Netflix Inc. (NFLX), which lets customers choose rental movies online and then mails them DVDs. Bear Stearns has a noninvestment banking relationship with Amazon.

Netflix shares recently lost 49 cents, or 2.5%, to $19.36. That stock set a year low of $18.59 on July 25.

A slew of companies have been rushing to make TV shows and movies available online now that media and entertainment companies have become more inclined to make their content available electronically. Long fearful of online distribution because of the potential for piracy, media companies have become more comfortable with piracy controls, known as digital rights management software. And digital downloads, because they don’t require packaging and shipping, could mean generous profit margins for content companies. Also, Hollywood studios are facing slowing DVD sales growth, which is encouraging them to consider new sales channels.

According to the terms-of-service document, customers will have to install an Amazon Unbox video player, which appears to be based on Microsoft Corp.’s (MSFT) player software, on their computer or portable player. Digital-rights-management software will restrict their ability to copy videos they buy and will delete expired rental videos. Customers who buy videos will be able to make a “back-up copy” on a DVD, but rights-management software will make it unplayable using a traditional DVD player, according to the document.

Customers also will be automatically shown trailers and other promotional content, although a bracketed note in the draft document suggested Amazon might give customers a way to opt-out.