(Fortune Magazine) -- Every problem is an opportunity, which makes the Hewlett-Packard mess one hell of an opportunity for CEO Mark Hurd. The big question for him and HP (Charts): Will he grab it?

Hurd is a terrific nuts-and-bolts operator and cost cutter, but that's only half of a CEO's job. Now he faces a huge chance to build the other critical CEO skills - those of a leader rather than a manager.

HP CEO Mark Hurd

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Should Hurd resign? Fortune Talkback forum HP CEO Mark Hurd says the buck stops with him, yet he isn't considering resigning. Meanwhile, HP's stock remains near the top of its 52-week range, despite the controversy. Is Mark Hurd still the right person to lead HP? (Tell us what you think)

When Fortune's Adam Lashinsky asked him about that (see the interview), Hurd seemed dismissive of big-picture leadership - in fact, seemed not to recognize what it really involves. He is by nature more focused on internal operations.

"I like being part of teams that go into things that people don't think are doing very well and getting into them to do better," he says. And "the other accoutrements, particularly the cocktail party/golf course circuit, and I don't mean to belittle that, is just not something I enjoy."

I don't believe he really thinks that drinking and golfing are all there is to the CEO's job beyond operations, but the comment suggests he'll resist growing into the kind of chief a $90-billion-a-year company needs. It's time for him to get outside his comfort zone. Four specific leadership moves would be great for the company and for Hurd. Here's his to-do list:

One of the ironies of this director-centered debacle is that HP's board seemed a picture of governance perfection. Yet this whole blowup originated in powerful, unresolved conflicts between board members, including former chairwoman Patricia Dunn and former directors Thomas Perkins and George Keyworth.

Minus those conflicts, it seems unlikely that Keyworth would have kept leaking information, as HP claims he did, or that some less slimy way of solving the problem couldn't have been found. Hurd must change the board culture radically. Every director has to put all his issues on the table, and anyone who isn't comfortable with that will have to go.

HP's brand will probably sail through recent events with barely a scratch. The scandal's greatest danger for the company is the effect on current and prospective employees. The HP Way, the code of behavior set down by founders Bill Hewlett and Dave Packard, is a living thing for many employees, and the first sentence says: "We have trust and respect for individuals."

That's not just corporate fluff. In a company of knowledge workers, trust keeps the place running. Hurd needs to get HP's leaders reenergized about the HP Way, debating it, rewriting it if they want, making it their own. Either that or throw it out. Just don't let it wither.

The job's previous holder, Ann Baskins, resigned on the morning she was scheduled to testify before the House subcommittee. She bears heavy responsibility for what happened, since her department was managing the outside contractors who did the pretexting.

She needs to be replaced with a lawyer who knows at least these two things: One, when you use private investigators, you must control them totally, since they have no conception of helping or harming larger corporate interests. And two, there's a lot more to the job than just staying within the law.

Baskins's lawyers insist that she firmly believed pretexting was legal. Who cares? It's sleazy, and for HP that's what mattered.

If prosecutors plan on bringing corporate charges, settling them will be worth whatever it costs. Hurd must also produce a victory for HP. A sexy new product, an interesting new alliance, just a great quarter - I don't know what it might be, but he does. The world needs something different and good to say about the company.

Hurd is on probation. The stock has done great on his watch, but if it falters, or if any other significant problem rears up, he's got no lifelines left. If he seizes his opportunities to grow, though, he could come out of this a stronger chief executive than he was going in.

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On Friday, Mark Hurd told Fortune's Adam Lashinsky that he's apologetic for approving a strategy of lying to the media, but stands by his instincts. Read the interview.