A storied financier of startups expands — but its new businesses have yet to take root.

A year ago, when venture capital firm Sequoia Capital ordered its portfolio companies to slash costs in the face of a sick economy, even healthy businesses, such as LinkedIn and Zappos.com, complied.

As word of the edict spread, many non-Sequoia startups also trimmed their budgets — a testament to the venture firm’s influence in Silicon Valley and beyond. In its 35 years in business Sequoia had nurtured the likes of Atari, Apple AAPL , Cisco CSCO , Yahoo YHOO , and Google GOOG . If it was bracing for the worst, the situation must be serious.

But just as Sequoia was commanding its upstarts to contract, the firm was plotting an ambitious expansion of its own. Throughout 2008 and into this year Sequoia tried entering entirely new businesses, hiring professional investors to build a hedge fund, as well as an asset-management group that would mimic the wealth-preservation approach popularized by major university endowments.

Sequoia has said little publicly about these new initiatives. Its preeminent partner, Michael Moritz, wouldn’t comment. He has good reason to remain mum: Both the hedge fund and endowment-like offering are off to exceedingly slow starts. The new initiatives have failed to attract a sufficient number of outside investors or even retain their initial high-profile employees.

More ominously, a nagging question lurks behind Sequoia’s entrepreneurial aspirations: What does it say about Sequoia’s commitment to the venture capital industry it helped invent if its partners are busy plotting entry into two corners of the financial services world in which Sequoia hasn’t the slightest bit of experience? In short, do Sequoia’s imperial ambitions confirm the venture world’s worst fears, that its best days are behind it?

Sequoia is hardly the only VC firm that is straying from its roots. Kleiner Perkins, which successfully seeded the public-private investment firm Integral Capital Partners nearly 20 years ago, has been busily focusing on “growth” and alternative-energy funds. New Enterprise Associates, a firm based in California and Baltimore, manages so many billions of dollars that it can’t possibly be considered merely a VC operation anymore. Sequoia itself had already broadened its offerings geographically with funds in Israel, India, and China.

What’s unique about Sequoia’s latest foray is the aggressiveness with which it has been expanding beyond the strategy that made it great. Sequoia began business in 1972 as a spinoff of Capital Group, the legendary fund management group in Los Angeles.

And for almost three decades Sequoia stuck mainly with venture investments. Even as its renown grew, Sequoia remained relatively small and focused. It put money into small, risky tech companies, and the size of its venture funds remained in the $400 million range, far below what competing firms raised. But this approach limited the fees Sequoia partners could earn — and the firm’s profit potential.

A few years ago, according to people in the know, Sequoia’s partners — chiefly Moritz and the other most senior active partner, Doug Leone — became convinced Sequoia needed to do more if it was to survive well into the future. Venture had passed through a golden age of relatively easy “exits” in the form of ubiquitous public offerings or sales to major tech companies. What’s more, the partners had accumulated immense wealth and weren’t satisfied with the various professionals offering to manage their money.

In 2008 Sequoia made its move. It hired Michael Beckwith, a seasoned hedge fund manager from Maverick Capital, a Dallas-based money management firm, and Eric Upin, the chief investment officer of Stanford’s endowment.

The plan was to raise two new pools of capital from Sequoia’s network — endowment investors in Sequoia’s venture funds, entrepreneurs whom Sequoia had helped become rich, and Sequoia’s partners themselves.

Its pitch? Sequoia’s existing funds would benefit from increased exposure to public-securities investments and the new clients recruited by the asset-management product, dubbed the Heritage Fund.

Sequoia’s timing couldn’t have been worse. Its expansion coincided with the worldwide financial meltdown — not a great time for a VC-turned-money-management-firm to raise funds. Without funds to manage, Beckwith and Upin left, the former back to his old firm and the latter to Makena Capital, an existing multibillion-dollar fund pursuing precisely the wealth-preservation strategy Sequoia coveted.

Sequoia hasn’t given up on its dreams, say people close to the firm. But it has scaled back its ambitions. Earlier in the year the firm abandoned swank office space in downtown San Francisco that was intended to house the Heritage staff, subletting the offices to a law firm.

The performance of Sequoia’s core business is a mixed bag. It has had some nice exits: Battery maker A123 Systems AAPL went public in September and is now worth more than $2 billion. Earlier this year Zappos.com agreed to sell to Amazon.com AMZN , and Cisco last year bought videocamera maker Pure Digital for $590 million. A potential home run is LinkedIn, whose investors have assigned it a billion-dollar valuation.

Yet in its most recent venture fund there isn’t one investment with the trademark Sequoia buzz. Some look promising, like mobile ad firm AdMob and Sugar Publishing, a producer of web content for women.

Others are duds, including online media companies Imeem and Joost. Sequoia notably isn’t invested in the hottest Internet companies of the moment, Facebook and Twitter, both of which seem, for now, to be gushers for their early venture backers.

True to form, Sequoia isn’t panicking. In September it gathered a group of friendly entrepreneurs and investing partners to update them on the firm’s progress. Moritz told the group that Sequoia remains committed to financing small, risky technology companies, with nary a mention of the new funds. Who would have thought Sequoia’s chanciest venture would have been its own?