The Old Testament was a time before Jesus when the Israelites went through their daily lives but in certain time periods there were prophets and holy men who interacted with God. (Which resulted in the books of the Old Testament).
Jesus came to fulfill the prophecies of the coming Messiah who would save all mankind from their sins, and when he came then all was fulfilled and all that is required of people is to believe in Jesus. There are no more prophets (John The Baptist was the last) as Jesus came and nothing more is needed than for man to believe in Jesus, that is our interaction with God through Jesus, prayer etc.
So why is there no more interaction with God such as described in the Old Testament? Jesus came and that was to fulfill everything. So all God wants of you is to accept Jesus.
With this being your view point do you view Islam as a false religon? Mohammed, according to the Quran, is a prophet of God. And if you do believe the Islam to be false what is your reason for believing so.