OK, that has an ATI graphics card, so it's not the known problem as that affected Nvidia cards only.
You could try going into the BIOS by tapping either F1 or F10 as soon as you turn it on using both the internal screen and an external monitor to see if anything comes up, if it doesn't then it may be a fairly serious problem....
Also try shining a torch at the laptop screen when it's on and look carefully to see if you can see a faint image, if so it may be the back light gone on the screen.