Pilgram, you have little faith my friend. I do not mean that to be a judgement against you but you are limiting the ability of our Almighty Father.
God is the same yesterday, today and forever...He is never changing. Everything was possible for Him in the early church days and is still possible for Him today. This includes, Healing, bringing people back to life, giving the gift of speaking in tounges, communicating with us through other sources than the Bible alone etc....
Speaking in Tongues is a spiritual gift from God and is absolutely still working in followers of Christ today. It is physical proof that the Holy Spirit is within you. Not everyone is blessed with this particular gift but everyone has a special gift that was meant for them.
As far as communicating with God by other means than the Bible alone, how do you believe the Bible was written? It is from God, but by human authors...if you believe the Bible is from God, you must believe God communicated with these authors. God most certainly "speaks" to us today. I personally do not hear God as an "audible voice" however I absolutely know when He is communicating with me. This is the "relationship" I am sure you often hear being referred to between man and our Savior.
I encourage you, Pilgram to read 1 Corinthians 14. As far as God not speaking to us...Do you pray? How does He answer your prayers? Not through the Bible....He communicates with us. I ask God for specific scriptures and He guides me right to them. There are plenty of way that God "speaks" to us. These are just a few thoughts....how do you feel about them?