How do I fix a blank screen during startup on my MacBook?

Left laptop overnight, as usual. Next morning, screen remained dark. Switched off using the power button.

Turning on, all I get is the start-up chime, but a blank screen.

At least, almost blank; it's possible to discern the start-up dialog box, when re-starting with 'command-R'

Also, have now discovered that, switched off, pressing any key will start up the laptop....

[Re-Titled by Moderator]

Original Title : Start-up problem