Determining when the legal right to sue has expired can be complicated. WA statutes of limitations for civil actions are mostly contained in Chapter 4.16 RCW (Limitation of actions). The statutes are at http://apps.leg.wa.gov/rcw/default.aspx?cite=4.16 .
The usual time periods for agreements are 3 years for unwritten agreements and 6 years for written agreements. However, there are many exceptions.
If the "contract" is to do something unlawful (such as killing someone), the court would not hear the case.
Depending on what the business is, there may be a regulatory entity specifically for the business. There may even be laws or rules specifically for the profession. For example, a WA attorney taking money and not providing the agreed services would likely be investigated and sanctioned by the Washington State Bar Association if the allegation is found to be true. The WSBA likely can investigate and impose sanctions regardless of how long ago the violations of ethical rules occurred.
What you should do is review your specific facts with your attorney to find out your legal options.