First, let me try to explain why they could conceivably try to collect from 18 years ago. The statute of limitations normally goes back to a starting date of when you first filed your tax return. However, if you never filed a return for the year in question, then there is no statute of limitations on that particular year. They can go back as far as they want to go back and try to collect the taxes due.
Having said that, I think your first step should be to side-step the collection agency and contact the State of Virginia Department of Revenue directly to find out exactly what transpired that makes them think you owe this debt. If you find that they really do have a legitimate claim for past due taxes, then you can try to work out a payment plan with them or even an offer in compromise, if they are willing to accept a lesser amount than what they claim you owe them. It is difficult to give much more advice than that beyond this point until you can determine the nature of their claim, but that would be your best starting point.
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I understand totally what you mean when you say it makes you uneasy to receive past due notices, particularly when they are telling you that you have 30 days to respond, "or else". But keep in mind that this is a collection agency that you are dealing with at this point and not the actual state of Virginia. Collection agencies will use whatever "scare tactics" they think will work to collect a debt, because that is how they make their money. But it is highly unlikely they are going to take you to court over a $3,000 debt, and if they did, it would certainly not be in the next 30 days. I hope this helps put your mind at ease somewhat.