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Without any other information (such as model and type of computer) I'm going to assume here that you are talking about a laptop.
Two primary suspects for that behavior from a laptop are:
1) Faulty Power Inverter for screen - you can check for this by shining a bright light at the screen and seeing if you can see a dim display - if there is a display, replacement of the screen or power inverter would be needed
2) Faulty graphics processor - you can check for this by connecting to an external monitor
If this is a desktop computer, please specify model number (which may be helpful in any case)