Matt Lockett was among those demonstrating outside as the Supreme Court opened its new term. Amid the shutdown, the court has said it will stay open at least through this week. (Matt McClain/The Washington Post)

The Supreme Court opened its new term as usual on the first Monday in October and went to work as much of the rest of the federal government was idle.

The court tackled two complicated business cases and disposed of hundreds of petitions that had accumulated over the summer. Among the cases the justices declined to hear was a request from Virginia Attorney General Ken Cuccinelli II (R) that it revive the commonwealth’s anti-sodomy law, which was struck down by the U.S. Court of Appeals for the 4th Circuit.

Chief Justice John G. Roberts Jr. did not mention the government shutdown as he officially closed the court’s 2012-13 term and opened its new one. The court has said it will remain open at least through this week and seems likely to hold two days of scheduled oral arguments next week.

The court is facing a docket filled with controversial issues such as abortion, affirmative action and the separation of church and state. On Tuesday, it will consider a challenge to campaign contribution limits that date to the Watergate era.

On Monday, the justices seemed unsure about a case arising from a Ponzi scheme perpetrated by R. Allen Stanford. The case is a class action brought on behalf of the 25,000 investors who purchased certificates of deposit from Stanford’s bank, based in Antigua.

Stanford promised a risk-free investment with above-market rates of return and said the CDs were backed by portfolios of liquid securities. In fact, there were no securities, and the money coming in went to support Stanford’s lavish lifestyle and acquisitions, and to pay interest to the existing CD-holders.

The scheme eventually collapsed. Stanford has been sentenced to 110 years in prison, and there is little chance for investors to recover their money from him or his companies. So they turned to state courts and filed suits against two law firms, insurance companies and financial service firms that helped in the sale of the CDs.

A district court said their effort ran afoul of a federal law passed to slow the growth of such class actions regarding securities fraud. The law attempts to prevent state law claims against third parties when the allegations are “in connection with the purchase or sale of a covered security.”

But an appeals court reversed that decision, saying the suits could go forward because the allegations were only “tangentially related” to covered securities.

“What was bought here was a CD,” said Washington lawyer Thomas C. Goldstein, representing those seeking to sue. “The plaintiffs here bought something that Congress specifically excluded” from the law.

Paul D. Clement, arguing on behalf of the third parties, said the Stanford Ponzi scheme was a “massive fraud.” But because the promise was that the investments were backed up with securities, the federal law blocking state actions should prevail, he said.

The Obama administration and the Securities and Exchange Commission seek a broad application of the federal law, which in this case puts them on the side of the defendants.

The justices asked tough questions of both sides, and it was hard to predict the outcome of the case. The combined cases are Chadbourne & Parke LLP v. Troice, Willis of Colorado v. Troice and Proskauer Rose LLP v. Troice.

In a second case heard Monday, the justices seemed frustrated. The case arose from a suit involving Harvey Levin, an assistant Illinois attorney general, who alleged age discrimination when he was fired at 61. The question was whether the federal Age Discrimination in Employment Act foreclosed Levin’s ability to file a civil rights claim under the Constitution.

But the discussion raised questions about whether Levin was covered by the ADEA or a different federal law. Several justices wondered whether they should try to decide the issue or send it back for more work in lower courts.

The case is Madigan v. Levin.