Pastor, I think we're arguing two very different things. I am saying God will not listen to all prayers, and you are saying He hears all prayers.
The Word is clear that the Lord will answer and fulfill prayers that are made in His Will and by a righteous heart. However it is equally clear that the prayer of an unrepentant heart will not be heard by the Lord and that our prayers are hindered by our sins.
If we simply peach one part of that, I think it's not laying out the need for salvation and sanctification to those not yet saved.