Well you could try hooking up an external monitor to it, while it is off, turn on the monitor and then turn on the laptop to see if the info shows on the external monitor. If it does, then it is probably the laptop screen. If it doesn't, well it could be the graphics card.
However, to be honest, if it is acting like this and it is brand new, you should really seriously consider taking it back to where you got it, or contact the manufacturer. It may be a defect and needs to be repaired or replaced. Never accept a faulty product.