I have moved because of a job. I cannot sell my house due to economy. Is there a tax deduction that I can receive because of rental in the new state where the new job is at?

You may be able to deduct moving expenses using Form 3903.
You may have to file tax return for both the states. Your U.S. Tax Return: Working or Living in Two or More states (http://taxipay.blogspot.com/2008/06/working-in-two-or-more-states.html)