Helmut,
What happens if you connect headphones or external speakers? Can the startup sound be heard then? Otherwise, there could be a problem on the logic board (this may be merely audio-related, or something more fundamental).
Even if a startup sound cannot be heard, nor anything seen on the screen, does the hard drive appear to be active (clicking, as during a normal startup sequence) after the computer has been turned on?
Have you tried using a magnifying glass to inspect the video and logic boards inside the computer (looking for leaking/bulging/discoloured/cracked electronic components)? Leaking electrolytic capacitors can be the cause of various problems.
You indicated that it is a 14" Mac monitor. Normally, that would mean a DB-15 plug (with 15 pins in two rows). Under your Older Hardware topic (https://discussions.apple.com/thread/6856695), you mentioned that the plug only had 10 of 15 pins. It is not possible to say whether or not the ten pins are sufficient without knowing their exact positions. Please note that special sense codes were used in order to tell Macintosh computers the type of monitor connected (you may want to search for "Sense Lines" at https://developer.apple.com/legacy/library/navigation/ for further information).
Could you borrow an older (CRT) PC monitor with a VGA plug (HD-15/DE-15, with 15 pins in three rows) just for a test?
Jan