The issues that brought Howard University to the brink of crisis last week remain unsolved, despite an unexpected "cooling off" period provided when Friday's blizzard sidetracked plans for a student boycott and canceled an emergency meeting of the trustees.

Janice McKnight, the campus newspaper editor whose expulsion prompted four days of demonstrations against university President James E. Cheek, said she returned to classes Wednesday and Thursday after a court order temporarily reinstated her.

But the school will seek to uphold the expulsion when the matter comes up for a new hearing, now set for Feb. 24, said Alan Hermesch, a university spokesman.

Hermesch said he knew of no plans to reconsider policies tightening controls on The Hilltop student newspaper or on faculty contacts with the press, the two main issues about which students have been protesting.

The demonstrations, led by the university student association, also involve a long list of other student complaints: poor housing, crime on campus, an "insensitive" bureaucracy and Cheek's relations with the Reagan administration, including his awarding of several honorary degrees to administration officials.

Cheek, who has been Howard's president for 13 years, made a brief appearance last Monday at an outdoor rally of protesters, and told them he would not give in to their demand that he resign. Since then he has made no statements on campus and has refused requests for interviews.

An emergency meeting of the 29-member university board of trustees, which had been scheduled for Friday morning, was called off late Thursday, and board chairman Geraldine P. Woods said she had no plans to call another special session.

"The president Cheek can handle the situation," Woods said in a telephone interview from her home in Los Angeles. "As it stands now, we support the president. We have no reason not to support him."

Another trustee, Edward P. Morgan, had strong praise for the embattled Cheek.

"He's done wonders for Howard in many ways," Morgan declared. "In terms of its image, he's taken it from the chaos of the 1960s and made a great, great contribution. I don't agree with him on everything. But he's done wonders."

Meanwhile, Joseph R. Applegate, chairman of the faculty senate, said a petition drive was under way for a special meeting of the senate, which includes about 1,500 full-time faculty members and administrators.

The 85-member senate council met with Cheek last Monday, Applegate said, but dissatisfied members, led by a group in the school of communications, were pressing for a meeting of the full group.

"There are a lot of concerns," Applegate said.

The current round of protests was set off when McKnight, a 23-year-old senior from Northeast Washington, was expelled after The Hilltop continued to give prominent coverage to a sex discrimination complaint against the university despite Cheek's urgings that the paper stop writing about the case.

Since she was no longer a student, Howard officials said, she could not edit the student newspaper.

They said McKnight was expelled because she gave untruthful information in her admissions application in 1979, concealing the fact that she had attended Syracuse University after high school and before she applied to Howard.

On Tuesday, D.C. Superior Court Judge George H. Goodrich temporarily reinstated McKnight as a student and as editor. Goodrich said it was "a mighty strange coincidence" that the expulsion followed the controversial articles.

The stories, which appeared in late fall, detailed charges filed with the Equal Employment Opportunity Commission by Michael Harris, a staff attorney who was fired Jan. 31. Harris contended in his complaint to the EEOC that Howard's general counsel Dorsey Lane favored female employes in pay and promotions.

In her request for the restraining order, McKnight said Cheek met with her twice in his office and asked her not to print anything more about the case, saying that the paper might lose university funds if the articles continued.

McKnight's complaint included an affidavit by her mother, Avis E. McKnight, who works as a clerk at Howard. Mrs. McKnight said Carl Anderson, vice president for student affairs, summoned her to his office and urged her to persuade her daughter to drop the Harris story. If the articles did not stop, she said in the affidavit, Anderson told her that her daughter "could damage her educational career at Howard University, her opportunities to attend graduate school and her opportunities to pursue a future career in journalism."

Neither Cheek nor Anderson has been available for comment on the accusations.

Over the past two years, the university, which receives much of its funding from the federal government, has lost jury verdicts in three lawsuits by dissatisfied employes and has settled eight other cases, involving a total of 15 professors and other employes.

The jury verdicts, two of which are on appeal, total $611,000. Sources familiar with the settlements say they have exceeded $200,000.

"Why have we lost so many lawsuits?" university student association president Howard Newell asked at one of the rallies last week. "What have they cost the university? How can we keep a general counsel with this record?"

Newell and other student leaders said the rallies and marches early last week were to have led to a class boycott on Friday. But those plans became moot when classes were canceled because of the snow.

Whether the boycott plans will be revived is uncertain.

McKnight said she thinks the students "will go ahead with it."

"The court put me back, not the university," she said. "The policies are still there. Dr. Cheek is still there, and he's still out of touch with the students. As far as I can see, nothing is settled."