I moved to New York State from the State of Virginia at the end of 2004. I worked in Virginia, paid Virginia taxes. I never worked in New York nor had any wages or income for the entire year. I filed my Virginia tax forms for that year. I did not file a New York State tax form as I never worked in New York. New York Taxation office sent me a letter demanding almost $4000 in taxes, penalties and interest for the year. I sent them proof and documentation that I only worked in Virginia and paid Virginia taxes. They have ignored the proof and copies of my Virginia tax form and still want the money. I only lived in NY for 22 days the entire year. What can I do and what can be done to get them off my back?

You were resident of NY for 22 days so the income for that period is subject to NY taxes. But this must be below the filing requirements. So you do not have any NY tax.

Write something like this "You were resident of NY in 2004 for 22 days from...
In 2004 you were not resident of Ny
In 2005 you were not resident of NY.

My income during 22 days in NY was below the filing requirement of NY. I do not owe any NY tax for 2004."

Get feedback from local tax professional. Do not ignore dates on NY letter.
Read: Your U.S. Tax Return: Working or Living in Two or More states

You will probably need to go see a NY state tax representative face-to-face to get this cleared up.

If you earned NO money during that 22-day period, and you can prove your move-in date as being 9 December 2004, then NY state has no legal standing to tax your Virginia-sourced income.