When I was a dub, I believed that Jehovah listened to everyone's prayers. But that was not the Watchtower position. It is very much supported in the Bible, though, as some have shown already.
I did have a personal experience where someone was praying to God as I showed up at their door. They were praying for the truth of the Bible. Back then, I thought it was holy spirit, Now I think it was probably coincidence. She is still a dub and doesn't know I have faded yet, as she moved away. Talked to her the other day and felt so compelled to get her out of that mess, but don't know how to go about it. I hate to think how this may end our friendship. We raised our kids together.
There have been times both as a dub and before I was a dub when I felt God answered my prayers. There have been other times when I felt nothing but deafening silence. But no one can tell me that I didn't have a relationship with God before I was a dub, because I know it is not true.
The arrogance of the society in putting their own conditions that have to be met in order for God to hear your prayers is sick. What happened to grace and the free gift of Christ's sacrifice? He is all of mankind's mediator, not just some select few that they choose.