The work’s not done, however. As HP CEO Mark Hurd has made very clear to everyone who will listen, HP’s division chiefs have marching orders to continue growing sales and profits in every product area – and that includes computers.

And that imperative, more than anything, is why the PC group last week unveiled the Blackbird 002.

At first blush, the Blackbird PC might seem like more of a museum piece than a serious product. At a time when a serviceable desktop PC with a monitor costs as little as $400, the Blackbird — no monitor included — starts at a whopping $2,500. That premium doesn’t come because the Blackbird is compact and portable, either. Its imposing, sculpted body hovers above a steel foot that’s capable of supporting more than 600 pounds.

So what’s the idea behind the Blackbird? In a word, luxury. HP is hoping to do for its PCs what Toyota did for its cars when it introduced the Lexus line. If the company can deliver a gorgeously designed product and offer top-notch customer service, maybe it will be able to change the PC business from a low-margin slog into a more vibrant adventure. And in the process, HP might just be able to boost its profits from selling computers.

HP’s not broadcasting it, but its role model for raising the PC’s profile is Apple (AAPL). Led by master marketer and CEO Steve Jobs, Apple has always managed to churn out innovative computer designs and convince its customers to pay a bit more for them. While most successful PC companies eke out single-digit profits per computer sold, Apple often manages to make more than 20 percent margins on each box.

Some of Apple’s margin magic comes because the company’s computers use Apple’s own operating system rather than buying the Windows OS from Microsoft (MSFT). But much of it also comes because of Jobs’s philosophy on the PC business – Apple doesn’t sell entry-level computers, which are important for grabbing volume and pumping up market share. “We just can’t ship junk. There are thresholds we can’t cross because of who we are,” Jobs said last month when he unveiled Apple’s new iMacs. “We don’t offer stripped-down, lousy products. We just don’t offer categories of products like that.”

Satjiv Chahil believes that HP might just be able to outdo Apple in the luxury game, while still selling entry-level computers. Chahil, who now heads marketing for HP’s PC division, has a track record of innovating in the consumer electronics business – he did marketing at Apple and Sony in the 1990s, and at Palm during its glory days at the beginning of the decade.

The Blackbird is the most visible example of the way Chahil is beginning to use design as he pursues his goal. I chatted with him about it in a house HP has built in the parking lot of its Cupertino campus, just a few minutes away from Apple’s headquarters. As we walked through rooms outfitted with home servers, flat-screen MediaServer TVs and digital picture frames, he talked about what he wants to accomplish.

HP’s Blackbird isn’t likely to be an overnight sensation – the $2,500 price tag will keep the masses away, and Chahil has decided to sell in online only for now, a decision that will keep people from experiencing the unique materials and design of the machine before they buy. But the lower volume will give HP room to be sure it delivers impressive customer service for the buyers of this high-end PC.

And if the HP gets it right, maybe its computer division can keep growing after all.