The SOL on credit card debt in Ohio is 6 years.
Tell them to **** off.
If you make *any* attempt to pay any of the bill, the SOL resets and it could reappear on your credit report. With debt that old, I usually tell people to just avoid it. If you're tired of dealing with the collection agency, you can write them a letter demanding that they stop and they are required by law to stop. At that point the only thing they can do is decide to sue you or not, which in your case I am 99% sure they cannot due to the SOL. Simply being contacted does not reset the SOL....only making an attempt to pay it does. This would be reflected on your credit report under something like Most Recent Activity, etc.