WASHINGTON, Jan 17 (Reuters) - The U.S. Supreme Court passed up the chance on Tuesday to hear controversial new cases about prayers before public government meetings and punishing students for Internet parodies or attacks made on computers at home.

The high court rejected appeals by local government and school district officials who argued that opening their meetings with prayers did not violate the constitutional requirement on church-state separation.

In one case, the justices let stand a U.S. appeals court ruling that predominately Christian prayers at the start of local Forsyth County commission meetings in North Carolina violated the constitutional prohibition on government endorsement of a particular religion.

The American Civil Liberties Union, which helped bring the legal challenge on behalf of two longtime residents, said it was glad the case now was settled.

"It is entirely inappropriate for government officials to endorse one set of religious beliefs over others by routinely opening public meetings with sectarian prayers," said Daniel Mach of the ACLU's Freedom of Religion and Belief Program.

In the other case, the justices declined to review a U.S. appeals court ruling that struck down the policy of a school board in Delaware of opening each meeting with a prayer, calling it an unconstitutional government endorsement of religion.

And in two other cases, the justices refused to take up the right of schools to punish students who create online parodies or attacks on school officials or other students from computers at home.

In one case the court turned down, a West Virginia high school student, Kara Kowalski, was suspended for five days in 2005 for creating a web page suggesting another student had a sexually transmitted disease and inviting classmates to comment.

Kowalski argued the suspension violated her free-speech rights and that school officials did not have the authority to punish her because she created the web page at home.

The justices let stand a ruling by a U.S. appeals court based in Virginia that school officials had the right to discipline Kowalski for harassing, bullying, ridiculing and demeaning another student.

That ruling appeared to conflict with one by a U.S. appeals court based in Philadelphia in a case from Pennsylvania about parodies of principals on the MySpace social network site.

The appeals court held the parodies were unlikely to cause significant disruptions at school and ruled for the students.

A high school student, Justin Layshock, created a profile of his principal in which he said he smoked marijuana, drank alcohol and engaged in lewd behavior. And an unidentified eighth grade student created a profile of her principal that said he enjoyed having sex in his office and propositioning students and parents.

The Supreme Court cases are Forsyth County, North Carolina v. Joyner, No 11-546; Indian River School District v. Doe, No. 11-569; Kowalski v. Berkeley County Schools, No. 11-461; and Blue Mountain School District v. J.S., No. 11-502.

For Forsyth County: David Cortman of the Alliance Defense Fund.

For Joyner: Katherine Lewis Parker of the ACLU of North Carolina Legal Foundation.

For Indian River School District: Jason Gosselin of Drinker, biddle & Reath.

For Doe: Thomas Allingham II.

For Kowalski: Adam Charnes of Kilpatrick Townsend & Stockton.

For Berkeley County Schools: Amy Smith of Steptoe & Johnson.

For Blue Mountain School District: James Ryan of University of Virginia Law School.

For J.S.: Witold Walczak of the ACLU of Pennsylvania.

 (Reporting By James Vicini)

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