When Freescale Semiconductor named Richard Beyer as CEO on Wednesday, many of my friends at the company felt the faint stirrings of hope. Freescale, which was spun off from Motorola in December 2004, is a kind of wallflower in the chip world.

It has some good products, but it also has some real problems that need solving before it can live up to the expectations set by its $17.6 billion buyout in September 2006. The buyout left Freescale saddled with$9.5 billion in debt. That’s a lot for a company that reported sales of $5.72 billion last year, down from$6.36 billion in 2006.

Freescale has three big problems. The first is that about a quarter of its sales come from its former parent, which is having a tough time all its own. The second is that it’s in so many markets — some of which are growing — while Freescale is standing still. The third and final problem lies in the fact that former CEO Michel Mayer was not the kind of leader needed to take a newly independent company down its own road.

Beyer may solve the third problem if he can step into his job in mid-March, listen to managers and figure out a strategy (likely involving a push to analog) that gets Freescale growing in step (or even ahead of) the markets it dominates.

To his credit, Beyer is walking into the job willing to listen. “It’s too early for me to presuppose that certain areas are the areas that we should focus on more,” he told me. As the CEO of Intersil, Beyer presided over several acquisitions and created a laser focus on analog chips. That strategy isn’t likely to work at Freescale, he said, which is too big in too many markets to pare down to just one.

As for the first problem, Freescale is trying to reduce the influence of Motorola on its earnings, but as Beyer points out, diversifying your customer base while continuing to satisfy your largest customers is a hard line to walk. “Motorola is very important to Freescale. We were its in-house semiconductor division and its objective was to serve the needs of Motorola, and serve the needs of others,” Beyer said. “What it doesn’t want to do is abandon its largest customer in favor of all other customers.”

Broad growth at the company, which reorganized its three market-defined product divisions into four product-focused ones at the end of 2007, may come if it can push deeper into the automotive segment, where it has a leadership position, and if it can take advantage of the transition to 4G cellular networks. There’s also the analog and sensor market, which Beyer knows from his days at Intersil.

Beyer managed to turn Intersil into a small but fast-growing analog company during his five years there. When asked what he thought Freescale’s growth opportunities were, he declined to get specific, but said, “I have some thoughts on areas where there are interesting opportunities by virtue of what I’ve been working on for the last couple of years.”

When pressed on analog and sensors, he said they were “certainly exciting.” Let’s hope Beyer can translate his excitement into growth.