For a short while, Atari tried to follow in
Apple Computer's lead and make
PCs.
Their first attempt in 1985, a year after the Macintosh, was a 16-bit Motorola 68000-based 520ST, internally dubbed the "Jackintosh." I don't think it sold too well, regardless of how well it performed. Public image was pretty bad. No business wanted to buy some "toy" PC from a "Game" company. Sales just never got up. They were pretty good for graphics I hear.
In 1986, Atari re-evaluated their strategy and the popularity of video games, in the wake of Nintendo and the NES (outselling Atari 10 to 1) and decides to release the 7800 game console.
In 1987 Nintendo's hold on the market grew, crowding out Sega and Atari. Atari released games for the 2600, which were all but ignored by the press, and released ports for the 7800--Namco's Galaga and Dig Dug, Robotron: 2084 and Joust, Electronic Arts' 1983 basketball game One-on-One Basketball, and Atari's own Asteroids and Centipede--that everyone had seen before. Nintendo released The Legend of Zelda on a cartridge in the United States, and cleaned up.
Later in the year, Atari decided that the PC world would never really welcome them, and instead repackaged their computer as a game console, the XE Game system, (XEGS). It used cartridges compatible with their older 8-bit computer line and included two games (Barnyard Blaster and Flight Simulator II), and a light gun and detachable keyboard. Sales were dismal.
In 1988, Atari established Tengen, a subsidiary that produced games for home consoles. Tengen began as a licensed third-party developer of NES-compatible games. This role ends when Atari Games took Nintendo to court, claiming that Nintendo had an illegal monopoly on the video game industry, achieved through illegal practices, such as fixing prices and using computer-chip lockout technology to prohibit unlicensed development of NES software.
You couldn't sell a NES cartridge unless Nintendo gave you permission, by licensing development and building in a lockout chip which wouldn't run the cartridge without the software key on the cartridge. Shortly after the initial lawsuit, Tengen somehow reverse-engineered the "lockout" and announced that they would manufacture games without Nintendo's consent. There wouldn't be a Nintendo Seal of Approval, but it would work...
One more unlucky move, in 1989 Tengen acquired the home rights to Tetris and began selling the extremely popular game. However, Tengen bought the rights from Mirrorsoft, which did not own the rights in the first place. While Tengen wrangled over this, Nintendo quietly acquired the legitimate home rights to Tetris and released it under its own label. The Tengen version is removed from the marketplace. Darn! Foiled!
Atari purchases the rights to a color console called the Handy Game and releases it as the Lynx ($149US), to compete with the runaway bestseller Game Boy. After publishing a handful of great Epyx games, Atari begins to develop a number of ports from the older Atari arcade games. More expensive than the Game Boy, the Lynx suffered from a lack of third-party support and was plagued by constant rumors that Atari would stop supporting the system.
In 1993 Atari tries to leapfrog past the 32-bit consoles of the time and introduces the Atari Jaguar system. It was the first 64-bit system bus. They stressed that it was made in the US, unlike some other consoles. I don't think it sold well because there just wasn't a lot of third party support behind them anymore. Most developers went for the bigger platform, like Nintendo or Sega. I don't know what prices and fees Atari charged, but it failed to get a huge following.
Plus, in 1994 Sony introduced the Playstation, which knocked the rest of the consoles off their feet. Poor Atari wasn't healthy already, and just couldn't stand up the same way Nintendo did.
Most information taken from The History of Video Games at http://gamespot.com/gamespot/features/video/hov/