What would cause compaq computer screen to go black

Welcome to Tom's Hardware Forums,
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)