I have been receiving correspondence from a company that bought a 10+ year old credit card bill that was 500.00, apparently they purchased it and it is now 2800+ dollars. I sent back the first 3 notices notifying them that the bill was 10+ years old and that I have received no correspondence in reference to this account in 8-10 years. They appear to be ignoring my correspondence, I just received the 4th notice, what is the law regarding statute of limitations on this in NY State?

You are misunderstanding what the SOL is. The SOL pertains to how long they have to institute legal proceedings against you. It has nothing to do with the expiration of the debt. Debts never expire. You signed a contract obligating you to pay whatever you charged against that card. That obligation still exists. Therefore, the owner of that debt has every right to dun you for it. If you want them to stop sending you dunning notices then work out a settlement.

Looks like it's 6 years...
Debt Consolidation Help & Relief in New York (NY) - New York City (NYC), Buffalo, Rochester, Yonkers, Syracuse
Some more info:
Statute of Limitations defense for disputing debts!

But as Scott pointed out, the debt does not go away.