There is a variety of things that could be going wrong with the computer, but there is a series of tests you could do to isolate the issue. Here's a question for you. Does the computer have a good battery? Does it continually shut off right after being turned on when plugged into a power source? Does the computer get past the HP logo and get to the Windows boot screen? And after the computer screen goes black, does the power light stay illuminated? These questions are all questions that will help isolate the problem.