Can I file a state tax return 4 years later, I moved to another state

Yes, but if you owe money be prepared to also pay interest on the payment.

Also, if the state return is tax year 2005 or earlier, and if you have a refund due, you have forfeited the refund, as all states with an income tax adher to the three-year statute of limitations for claiming refunds that the IRS follows.