In order to be able to help you better I need additional information regarding the error that you receieved on your screen before it turned black. Did you recieve any error code when the blue screen appeared?
Have you made any changes on your laptop prior errors?
I also would like to know if the hard drive is spinning during the black screen appearance. If it does, then probably the fault is with your videochip. If it doesn't, well I guess you have to try it in another PC via connecting it with SATA-USB cable and if it does not respond, you might think of an replacement.