I remember this book from my early teen years, although what I remember makes it seem incredibly bizarre, but from what I remember, it was really enjoyable. I'm sure I read it before I read the "Mister Monday" series, by Garth Nix. I don't believe all of the series was available, if that helps narrow down a time frame. I have a feeling this book was part of a series too. And it is based around a young male protagonist and, soon, a girl and another boy, whom he befriends. I believe the first chapter of the first book starts with the protagonist answering a phone call. One of the questions he is asked is; How did the dinosaurs die? He initially believes this to be one of those radio shows, so he tries to be funny in his answer, which is; they died laughing. I'm sure they ask him about his sleeping habits, and he admits to falling asleep very easily, almost on command. This leads the boy to being recruited by an organisation which uses sleep as a way of entering and exiting some sort of world, or other time. There is something dangerous about it too, as I remember something about: trying to go deeper, or further, caused the person's heart to race to the point of an attack. When he first travels to this place, it's like the beginning of time. The place is beautiful, and untouched. The protagonists male friend befriends a black panther cub, which I'm sure follows him around when they return.
This is when I lose track of the story and just remember snip bits;
The male friend is a skilled drummer and is able to tap into the 'beat' of the world, and stop time from travelling backwards - I believe this is in the second book. The female friend is a skilled debater with unmatched logic, and during an argument with (some sort of boss bad guy), she uses the argument of a never ending cycle, a snake biting its tail. I'm sure she also had a bracelet of a snake biting its tail too, with green eyes? There is a point where they are traveling through a cave of jewels. The protagonist collects some. They then come to a seemingly dead end, however, by giving up everything they covet, such as the jewels, the characters are able to ascend to the village above.
Sorry for the long post, but I thought adding as much as I know might spark an answer from someone. :).
Thank you for your time.