Double check that the cable between the computer and monitor is correctly inserted at both sides.
There may be some corrosion or the contacts may be dirty.
Disconnect and reconnect a few times.
The cable may be damaged. Try with another cable.
I can offer one suggestion that may help and that is to check the power supply transformer, as this may have failed.
Try using a different transformer and see if that fixes the problem. You'll probably have a suitable spare transformer somewhere in the house, by locating any other electronic devices that also have transformers, and then see if you can find one that has the same voltage output and same sized connector. If you do, double check the polarity of the connector is the same too. (This polarity info will be on the transformer label and is a little diagram that has a dot with a circle or C shape round the dot and two straight lines each leading to a plus or minus sign) make sure this diagram is the same if trying a different transformer.
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