I read this book about 8 years ago, before they renovated our library. It is written by an Asian author (Japanese I think), and is heavily influenced by Asian cultures.
The main character's parents are divorced; the father cheated on the mother because she is sick and dying. The main character is upset and wants to cure his mother so much that he makes a wish and is given the opportunity to grant his wish by questing through an alternate world and gathering magical stones. The catch is that he is competing against another character who also has a wish, but only one wish can be granted.
I remember that the only way to enter the fictional country was to go up stairs that lead to nothing (the main character uses a stairway at a construction site), and one of the companions he meets along the way is a lizard person.
Physically, I remember the book being really large and having a teal cover with some cartoonish art of the main character and his companions.