Is there a statute of limitations on being fired for a wrongdoing?

The incident for which I was recently fired actually took place over a year and a half ago. I had been with the company for 8 years without any problems or incidents. I agreed to the incident and asked if it was a firing offense to which the human resource investigator read the list of firing offenses and said "no, that it was not listed but I might be setting a prescident". I asked the manager what he thought and if I should be worried and he said it would prob. just be a write up. He called me in early the following Friday and fired me. I would like to know if there is a statute of limitations on when something took place that a company can fire you for. They said I violated company policy but it is not listed in the company policy. They also appear to be making every attempt to block my appeal through an open door policy that the company has in place. I was told(by the human resourses person that did the investigation) I could not appeal because it was a violation of company policy however when I call associate relations, they said I can. Also, the manager that fired me had an incident that took place after mine which was along the same lines but way worse than mine and was investigated before I was and nothing happened to him. Any suggestions would be greatly appreciated. Thank you!!