Is prayer to Jesus required for salvation? According to the Bible, will those who have heard about Jesus (and, perhaps, even believed that Jesus existed or that he had a special role) and yet have never prayed directly to Him (i.e. never addressed Him in prayer by using the name "Jesus") go to hell?
There's an old saying (more or less) in Christianity that it's not a religion, but a relationship.  There is biblical support for this coming from this verse:


  Matthew 7:21-23 (NIV)
   “Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but only the one who does the will of my Father who is in heaven. Many will say to me on that day, ‘Lord, Lord, did we not prophesy in your name and in your name drive out demons and in your name perform many miracles?’ Then I will tell them plainly, ‘I never knew you. Away from me, you evildoers!’


Very simply, it's not just what about is in our hearts; nor is it about what we do; it's about having the relationship with Jesus.  

Without prayer, there is no relationship (and can be no relationship).  Without prayer, we cannot make ourselves known to God.


  Phillipians 4:6 (NIV)
  Do not be anxious about anything, but in every situation, by prayer and petition, with thanksgiving, present your requests to God.


Phillipians shows that if we do not pray, our requests won't be presented to God and so he will (as stated in Matthew) not know us.