"St. Cyprian of Carthage writing to Pope Cornelius of Rome said that the Saints should keep praying for one another even after some depart to be in the presence of God. And that is all that the Orthodox want to do is ask the Saints to keep praying for us."
Was Cornelius dead when Cyprian wrote to him? No, he wasn't. Asking a living person to pray for you after he dies isn't equivalent to praying to the deceased. See here and here for some discussions of the evidence against praying to the dead.
And is it true that "all that the Orthodox want to do is ask the Saints to keep praying for us"? No, that's not true. Here, below, are some examples of prayers to Mary in Eastern Orthodoxy. Notice that they do much more than asking Mary to pray for them. And even if they did only ask her to pray for them, the practice would still involve praying to the deceased, something the earliest Christians knew nothing about and sometimes condemned.
Here's an example of a prayer to Mary:
Rejoice Mary, Mother of God, Virgin, full of grace, the Lord is with thee: blessed art thou among women and blessed is the Fruit of thy womb, for thou hast borne the Savior of our souls. Meet it is in truth, to glorify thee, O Birth-giver of God, ever blessed, and all undefiled, the Mother of our God. More honorable than the Cherubim, and beyond compare more glorious than the Seraphim, thou who without stain didst bear God the word, true Birth-giver of God, we magnify thee.
O gracious Mother of the gracious God, O most pure and blessed Mary, the Mother of God, pour the mercy of thy Son and our God upon my impassionate soul, and with thine intercessions set me unto good deeds, that I may pass the rest of my life without blemish and, with thine aid, attain heaven. O Virgin mother of God, the only one who art pure and blessed. O Queen of the Heavenly Host, Defender of our souls: being delivered from evil, as thy servants, O Mother of God, we offer unto thee the hymns of thanks and victory; but as thou hast power invincible, deliver us from all calamity, that we may cry unto thee: Rejoice, O ever-Virgin Bride!
O virgin, spotless, undefiled, unstained, all-chaste and Pure Lady, Bride of God, who by the glorious birth-giving hast united God the Word with Man and linked our fallen nature with Heavenly Things; who art the hope of the hopeless, the helper of the oppressed, the ready protection of those who haste unto thee, and the refuge of Christians; despise me not, who am defiled and sinful, who by my wicked thoughts, words and deeds, have become an unworthy servant, and by my slothfulness have turned into a slave to evil affections. O Mother of the God of Love, have mercy and compassion upon me, a sinner and a prodigal. Accept this prayer which is offered to thee from my impure lips; and putting forward thy maternal influence with thy Son, my Lord and Master, beseech Him to open unto me the lovingkindness of His grace; beseech Him to overlook my countless transgressions, to give me true repentance and to make me to be a zealous doer of His commandments. And thou, being gracious and compassionate and tender-hearted, be thou ever present with me in this life as my defender and helper, so that I may turn aside the assault of my enemies, and guide me into salvation; help my poor soul at the hour of my death, and drive far from it all the dark forms of the evil ones. And in the dreadful Judgement Day, deliver me from everlasting punishment, and present me as an inheritor of the ineffable glory of the son, our God.
O may I obtain this, most-holy Lady and Birth-giver of God, through thine intercessions and mediations, by the grace and exceeding great love of thine Only-Begotten son, my Lord and God and Savior, Jesus Christ, to Whom is due, with the eternal Father and the All-Holy, Good and Life-Giving Spirit, all honor and glory and worship, now and ever, and unto ages of ages. Amen.
O most glorious Ever-Virgin Mary, Mother of Christ our God, accept our prayers and present them to thy son and our God, that He may, for thy sake, enlighten and save our souls. (source here)
Tenderness springs forth from you, O Theotokos, make us worthy of
compassion. Look upon sinful people, reveal your power for ever as we hope in
you and cry aloud: Hail! as did the Archangel Gabriel, Chief Captain of the
Bodiless Powers. Amen. (source here)