Yahoo has been trying to find itself for the last several years, while its stock price has been pummeled in the wake of Google’s rise and Microsoft’s aborted takeover attempt. Has it found itself?

Yahoo CEO Carol Bartz’s microphone cut out right as she began to respond to the question, “What is Yahoo?”, posed by TechCrunch founder Michael Arrington in an combative onstage interview today at the Disrupt conference in New York. The irony of the moment prompted audience mockery that set the tone for the rest of the interview.

Once her sound was restored, Bartz delivered a confused quote that made it sound like the company is still very much adrift.

“Yahoo is a great company that is very, very strong in content for its users,” Bartz told Arrington. “It uses amazing technology to serve up what we increasingly think is going to be the Web of One.”

Both interviewer and interviewee traded insults as Arrington pressed Bartz to explain the company’s direction. The clearest comments Bartz made centered around personalization. Yahoo wants to run a site that users visit every day, and it wants to provide tailored content and advertising to visitors.

Eventually, Arrington asked Bartz if Yahoo is a search company. “Half of our revenues and profits are from search,” Bartz responded. “Crawling and indexing the Web is a commodity.”

What emerged over the course of the interview is that Yahoo has its hands in many areas but doesn’t own any of them. Bartz frankly admitted that she would like to have Facebook’s control of the social graph or Google’s search dominance.

She came off defensive and abrasive in response to taunting, demeaning questions from Arrington. Bartz pointed out that it took Apple CEO Steve Jobs about seven years to turn the Cupertino company around after retaking his spot at the helm. “Seven years,” Bartz said. “I’ve been at this company 15 months. Come on.”

Yahoo needs to find itself fast, but Bartz does have a point that it takes time to define a company’s direction. And it sounds like the company’s employees have a fierce defender in the current CEO. “I don’t want to hear any crap about something magical that the fine people of Yahoo are supposed to do in this short period of time,” Bartz said.