How to deal with state government extortion?

I lived in state "M" until 1998. In 1999, I moved to NYC. In 2000, "M" sent me a letter claiming I owed them $700 in taxes for 1999... I told them I lived in NYC. They wanted proof. I sent them copies of my 1999 W2's. 2-3 weeks later, still no response. I called them again. They said they never got my letter. I had to moved 6 times bet. 1999-2000. Getting my mail wasn't easy, things were a little hectic. I forgot about the "M" case. A couple years later, they sent me a new bill: $1,400. I threw it away. 4-5 years ago, I checked my credit report for the first time. The "unpaid tax" was there, to stay. I decided to end this non-sense, but now the case is gone. I read that most cases have an "expiration" date, but if you call the other party, then it's back to square one. Any advice? Thx