Jeroen Meerbach, I am not a Mac person, so take this answer as something to try until the Mac gurus give you a more precise answer. Just reread your question and noticed you already tried to reset SMC and PRAM :-)T
Your iMac also has some diagnostic LEDs. Take a look at those and see what, if anything shows
Depending on iMac model, there are either three or four built-in diagnostic LEDs on the logic board that can help troubleshoot the computer. LEDs are located on bottom right edge of logic board (under a piece of black mylar tape) and can only be seen when looking through lower vents of rear housing.
• Indicates that trickle voltage from power supply has been detected by logic board. This LED will remain ON whenever the iMac is connected to a working AC power source. The LED will remain on even when computer has been shut down or put to sleep. The LED will turn off only if AC power source is disconnected or power supply is faulty.
• Indicates that logic board has detected power from power supply when computer is
turned on. This LED will be ON when computer is turned on and power supply and voltage regulators are working correctly.
• Indicates that computer and video card are communicating. This LED will be ON when computer is communicating properly with video card. If LEDs 1 and 2 are ON and you heard the startup sound, but LED 3 is OFF, then video card might be installed incorrectly or need replacement. Note: LED #3 is not present on models with integrated graphics.
• Indicates that computer and LCD panel are communicating. This LED will be ON when computer is turned on and video signal is being generated. If LED 4 is ON and there is no image on display, then LCD panel, LED backlight board, or cables between might be installed incorrectly or need replacement.
Hope this helps, good luck.