I think it's interesting that so many of the Psalms begin with - or at least towards the beginning - have the phrase "God, hear my prayer" or something similar. My guess is that this was a common phrase of the day that you used when you approached God. I don't think it was spoken from a lack of faith or with the thought that God wouldn't pay any attention if you didn't say that first. You can always see that the psalmist had faith because he says things like "God is my helper; the Lord is the sustainer of my life. v.4
Many times the things we say in prayer are a reminder to ourselves of things that God has said. So I'm thinking that as David or whoever was praying and writing out the Psalm as a prayer the phrase "hear me, "listen to my voice," "give ear to my words," were a reminder that you weren't just thinking to yourself or wishing on a star, but you were talking to God, Himself.
As I was typing that paragraph a verse came to mind that the people of the Old Testament couldn't experience. It's an encouragement we have to come before God because of what Jesus Christ has done for us.
Hebrews 4:16 Therefore let us draw near with confidence to the throne of grace, so that we may receive mercy and find grace to help in time of need. NASB
The King James Version uses the word "boldly"
16 Let us therefore come boldly unto the throne of grace, that we may obtain mercy, and find grace to help in time of need.
What an awesome thought. We don't have to plead, "Lord, PLEASE listen to me!" We can come with confidence, knowing Jesus has made us right with God and therefore we can come to Him with confidence, knowing He will hear us.
That should make a difference in how you pray today (and tomorrow, and the next day and all day long....)