Meditation is prayer.. Being still, quiet and listening is an important part of prayer.
Communion and fellowship is prayer.
God is a person, relationship with him is prayer. Communicating is a two way activity. When you pray can God get a word in?
Are you going through the rituals? Or are you being real with Him as a real person?
There is a place for asking. But prayer is more than that! Praise is also prayer. Sometimes just being there together is prayer!
Approaching him as a father who is not mad at you... That is prayer! As some one you are comfortable to be with, some one you respect and are not afraid of... That is prayer.
It is not true that your only purpose is to serve God... God created us for his pleasure, he just loves us and wants to have an intimate relationship with us, not for us to do anything for him. He doesn't need anything from us, but he wants us anyway.
Psalm 46:10 KJV
 Be still, and know that I am God: I will be exalted among the heathen, I will be exalted in the earth.
Isaiah 54:9-10 KJV
 For this is as the waters of Noah unto me: for as I have sworn that the waters of Noah should no more go over the earth; so have I sworn that I would not be wroth with thee, nor rebuke thee.  For the mountains shall depart, and the hills be removed; but my kindness shall not depart from thee, neither shall the covenant of my peace be removed, saith the Lord that hath mercy on thee.
Joshua 1:8-9 KJV
 This book of the law shall not depart out of thy mouth; but thou shalt meditate therein day and night, that thou mayest observe to do according to all that is written therein: for then thou shalt make thy way prosperous, and then thou shalt have good success.  Have not I commanded thee? Be strong and of a good courage; be not afraid, neither be thou dismayed: for the Lord thy God is with thee whithersoever thou goest.
Philippians 4:6 KJV
 Be careful for nothing; but in every thing by prayer and supplication with thanksgiving let your requests be made known unto God.
Luke 12:32 KJV
 Fear not, little flock; for it is your Father's good pleasure to give you the kingdom.