I''m teaching high school business law and I am somewhat unclear on contract law. Is it possible for a contract to be valid yet unenforceable in court?

Yes.  The contract could have an arbitration clause preventing the litigation of a breach in any court.  The litigation would then be done through arbitration.  Also, the statute of limitations may have run, leaving a valid contract which cannot be sued upon. This is not intended to be legal advice, and is general in its nature. No attorney-client relationship exists or is formed by this information. Furthermore, this does not represent the views or opinions of LexisNexis or its affiliated companies.