When Apple (AAPL) updates an aging computer, it usually keeps the price the same and bumps up the specs — increasing processor speed, disk capacity, built-in memory, etc.

Not this time. The new Mac mini, which quietly popped up on Apple.com early Tuesday alongside the higher-profile iPhone 4, starts at $699, $100 more than the previous model and $200 more than the original.

When Steve Jobs first introduced the Mac mini at Macworld 2005, he described it as the “most affordable Mac ever” — a stripped-down $499 box designed to lure Windows users to the Mac side. It was strictly BYODKM … bring your own display, keyboard and mouse.

“People who are thinking of switching,” Jobs said, “will have no more excuses.”

But switchers, it turned out, tended to buy Apple notebook computers, and in the years that followed the mini morphed into something more like a media server, used primarily to deliver music and video to home entertainment systems. Last fall, Apple began offering a $999 Snow Leopard server edition that came with a terrabyte of hard drive.

This year’s edition $699 has a new 1.4-inch thick aluminum unibody design, a 2.4GHz core duo chip, a 320GB hard drive, 2GB of memory, an 8x double-layer SuperDrive, NVIDIA GeForce 320M graphics, HDMI-out and an SD card reader for digital cameras. The $999 server model comes with a pair of 500GB hard drives, a 2.66GHz processor, 4GB of memory and no SuperDrive.

“This is the most significant form factor change for the Mac mini since it was introduced,” writes Kaufman Bros.’ Shaw Wu in a note to clients issued Tuesday. “The only disappointment we have is the price point of $699.”

See Apple’s press release for more detail.

[Follow Philip Elmer-DeWitt on Twitter @philiped]