Hey @GuillaumeSTEIN, thanks alot for your help, and also thank you for describing your solution to your post!
Unfortunately, I couldn't make it work. Nothing happens on the Arduboy, I tried it again and again. Also, you said "First try to check if your card shortly appear in the port list of the Arduino IDE", but the port list only displays "COM1", no matter whether the Arduboy is even connected or not, turned on or off etc.
There's not the slightest hint on my PC that even Windows recognizes a device on the USB port, no device in the device manager etc.
Again, every help is appreciated!