You filed your 2006 federal income tax return in April 2010 Will the IRS still pay you your refund after 4 years?

Yes if this was Before April 15, 2010. Three year from the due date of the 2006 income tax return which was due by April 15 2007. After April 15 2010 any refund that may have been due you was no longer available to you after that date.