Here is a comprehensive and well written case from NJ which discusses when a statute of limitations starts to run there.  NJ, unlike NY has a "discovery" statute of limitations. DIANNE VIGLIONE v. CHRISTINE FARRINGTON, ESQ.,

"A legal malpractice action is based on negligence. Grunwald v. Bronkesh, 131 N.J. 483, 492 (1993). A cause of action for malpractice usually "accrues when an attorney’s breach of professional duty proximately causes a plaintiff’s damages." Ibid. This occurs when a plaintiff "detrimentally relies on the negligent advice of an attorney." Id. at 495. The timeliness of a complaint for legal malpractice is governed by N.J.S.A. 2A:14-1; McGrogan v. Till, 167 N.J. 414, 417 (2001). The statute requires that a legal malpractice action commence within six years from the accrual of the cause of action. Id. at 424-26; Grunwald, supra, 131 N.J. at 499.

While the above formulation may seem to provide a bright-line rule, the Court has recognized "the unfairness of an inflexible application of the statute of limitations when a client would not reasonably be aware of ‘the underlying factual basis for a cause of action.’" Vastano v. Algeier, 178 N.J. 230, 236 (2003) (quoting Grunwald, supra, 131 N.J. at 492-93). To protect such uninformed clients, the Court has adopted a discovery rule in situations where the injury is "not readily ascertainable." Ibid. On this point, the Court has explained:

Without the discovery rule, the limitations period would run from the occurrence of the negligent act. Therefore, a scoundrel would have an incentive to conceal material facts from or to misrepresent those facts to the client so that a malpractice claim would be time-barred. Applying the discovery rule to legal-malpractice actions will remove the incentive to deceive and thus will preserve the fiduciary duty of full disclosure. [Grunwald, supra, 131 N.J. at 494.]

The Court concluded that the statute of limitation period for a legal malpractice claim, in these circumstances, does not run until "the client suffers actual damage and discovers, or through the use of reasonable diligence should discover, the facts essential to the malpractice claim." Vastano, supra, 178 N.J. at 236 (quoting Grunwald, supra, 131 N.J. at 494).

"The linchpin of the discovery rule is the unfairness of barring claims of unknowing parties." Caravaggio v. D’Agostini, 166 N.J. 237, 245 (2001) (quoting Mancuso v. Neckles, 163 N.J. 26, 29 (2000). Thus, "[i]n applying the discovery rule, a court must determine when the plaintiff became aware of the underlying factual basis for the legal-malpractice action." Olds v. Donnelly, 150 N.J. 424, 437 (1997). "