I downloaded High Sierra on a MacBook Pro already running 10.13.6 and then quit the App Store. No installation window appeared. What does ‘close the App Store’ mean?

I have a G4 Quicksilver problem that isn’t quite any of the above. Computer turns on and boots up normally but then cuts out after two or three minutes to black screen and unresponsibve keyboard and mouse with On/Off light on Apple Cinema display blinking rapidly. No reponse from holding down power buttons on display or on front of G4 tower. Only ‘fix’ is to unplug power cable and start again. Any ideas?