I find it curious that no one mentions the one instance where a prayer is explicitly mentioned as being silent and it was answered.
1 Samuel 1:9-19 (NLT)
9 Once after a sacrificial meal at Shiloh, Hannah got up and went to pray. Eli the priest was sitting at his customary place beside the entrance of the Tabernacle. 10 Hannah was in deep anguish, crying bitterly as she prayed to the Lord. 11 And she made this vow: “O Lord of Heaven’s Armies, if you will look upon my sorrow and answer my prayer and give me a son, then I will give him back to you. He will be yours for his entire lifetime, and as a sign that he has been dedicated to the Lord, his hair will never be cut.”
12 As she was praying to the Lord, Eli watched her. 13 Seeing her lips moving but hearing no sound, he thought she had been drinking. 14 “Must you come here drunk?” he demanded. “Throw away your wine!”
15 “Oh no, sir!” she replied. “I haven’t been drinking wine or anything stronger. But I am very discouraged, and I was pouring out my heart to the Lord. 16 Don’t think I am a wicked woman! For I have been praying out of great anguish and sorrow.”
17 “In that case,” Eli said, “go in peace! May the God of Israel grant the request you have asked of him.”
18 “Oh, thank you, sir!” she exclaimed. Then she went back and began to eat again, and she was no longer sad.
19 The entire family got up early the next morning and went to worship the Lord once more. Then they returned home to Ramah. When Elkanah slept with Hannah, the Lord remembered her plea, 20 and in due time she gave birth to a son. She named him Samuel, for she said, “I asked the Lord for him.”
Hannah's prayer was silent, but the Lord answered her with the birth of Samuel. Considering warren's answer, there is no reason not to believe that silent prayers are answered in modern times as well.