The Virginia General Assembly, forced by a broken computer to conclude its 1983 session a day late, voted today to create an intermediate court of appeals that for the first time will guarantee convicted criminals a second hearing in the state's courts.

The nine-judge court also is intended to relieve the state Supreme Court's crowded caseload and reduce the waiting time for appeals, now more than two years in many cases. Until the court begins sitting in 1985, Virginia will remain one of two states where individuals convicted of state crimes have no automatic right to a hearing in a higher court.

The court proposal unexpectedly emerged as one of the most controversial issues of the session, with opponents labeling it a "lawyers' relief bill." Gov. Charles S. Robb gave it a lukewarm endorsement in his opening address to the legislature, but then lobbied hard for the measure in final days of the session.

He met with a conference committee over the proposal close to midnight Saturday, but he had to settle today for a bill that would exclude civil lawsuits from the new court's jurisdiction.

The legislature, in a session that lasted about three hours, also agreed today to restore $55 million in cuts that Robb had proposed to the state budget--mostly in public education and salaries for state employes. The workers will get a minimum 5 percent increase in take-home pay under the plan approved by the legislature.

It was the budget, hammered out during three days of hard bargaining between House and Senate conferees, that kept the legislature in session an extra day after a computer at the Divison of Motor Vehicles crashed late Saturday. It was printing copies of the 65-page budget compromise and without those documents the assembly's leadership extended the session and called the membership for a rare Sunday morning meeting.

Disgruntled legislators, many of whom already had begun celebrating the end of the session, had to unload their cars and return to their hotels. By 12:45 p.m. today, the legislature's work was done.

The budget, billed from the start as this year's main legislative issue, was approved with little debate in the Senate on a 33-to-5 vote and in the House by a vote of 91 to 6.

There were a few muffled complaints about the lack of time legislators were given to review the complex document, and Del. Warren G. Stambaugh (D-Arlington) objected that parts of the budget overrode other bills the legislature had passed.

"What I have objections to is making the House Appropriations Committee and the Senate Finance Committee into supercommittees," said Stambaugh. "It's not just a question of dollars, but a question of the policy of the legislature."

This year was the first time the Senate drafted a budget proposal of its own, an innovation roundly condemned by House Appropriations Committee Chairman Richard M. Bagley (D-Hampton). "I would never again be willing to accept a double budget process," he said today.

Overall, the House's version of the budget prevailed: Almost of Robb's proposed $20 million cut in local school aid was restored, $7 million was put back in for colleges and universities and the state obligated itself to pick up employes' contributions to the retirement system--at a cost of $30 million.

The court proposal will give the General Assembly and its Democratic majority nine extra judgeships to fill next year. "It's a nice piece of patronage for the Democrats," said Sen. Ray L. Garland (R-Roanoke). "All their ex-members go on to become lobbyists or judges, and this will certainly help them find their just rewards."

Yet when they left here today, the legislators left behind a vacancy on the state Supreme Court, after the House and Senate Democratic caucuses endorsed different candidates for the job.

The appointment to the seven-member bench now goes to Robb although some legislators were hoping they could try again for a compromise when they come back for a one-day veto session in April.

Proponents of the new appeals court argued that justice is ill-served by the current system, with convicted criminals and those who lose civil suits standing less chance of having their appeals heard than in almost any other state. Supreme Court justices often refuse to hear an appeal, they said, after a cursory review of the file by a junior court attorney.

The system gives unusual power to local trial court judges, whose decisions are rarely questioned, and some legislators -- who elect all judges in Virginia -- were reluctant to dilute their authority. "We have had a tradition in Virginia of circuit judges being powerful and insulated individuals," Garland said.

Supporters and opponents of the court spent more than eight hours Saturday in what Sen. Edward M. Holland (D-Arlington), sponsor of the bill, called "a real rassling session" of a conference committee. They emerged with a hybrid proposal that satisfied few in the Senate but was termed by proponents a significant beginning.

The Senate approved the new court by a vote of 24 to 14 and the House passed it by 69 to 30.

"It is probably not quite as bold a step as originally envisioned," said Sen. William F. Parkerson Jr. (D-Henrico), chairman of the Senate Courts Committee. "But it does provide significant relief to the Supreme Court ."

The court will hear appeals of criminal and domestic cases but, unlike in Holland's original proposal, not civil lawsuits. Instead of Holland's proposed 12 judges the court will have nine meeting in three-judge panels around the state, probably including Northern Virginia.

The compromise means that Virginia, one of two states in the country that does not currently grant an automatic right to have appeals considered, will now allow that right in criminal but not civil cases. Sen. Joseph V. Gartlan Jr. (D-Fairfax), who had campaigned for the appeal by right, said he was disappointed.

"It has all the problems of a compromise," Gartlan said. "It will fail to address a significant part of the judicial administration problem. But I'm confident we'll be able to do more over the years."