Step 1: What the problem could be
Here is how to open it and possibly fix the problem.
I must tell you , this laptop suffered from a shorted out wire before this problem. I had to replace the power cable, inside the computer, between the screen and the power supply.
I had heard of people on the web, replacing there batteries with the same problem. Before trowing out that battery, or exchanging it from a refurbishing place, have a look at the fuse.