dsi won't turn on

My daughter's dsi won't turn on I've checked the ports bought new chargers and everything. I plug it in and the charge light is blue. Thought it might be the battery but I want to be sure. I just bought her new games for Christmas and she will be disappointed if she can't play it. The screen won't turn on. If I press the start button the blue charge light goes out off and on the charger. Please help!

Barbara