Ok, finally I got it solved!
The key is just to use a "good" USB cable - that's all! I tried three cables from the same brand, all had shown the same problem. But finally I've tried another one from a Sony smartphone and this does really work.
I think it's really the quality of the power through the USB cable. And I think it could also be fixed by an external PSU. With the bad USB cables the boot process at the point where it accesses the eMMC, maybe this operation needs more power than provided.
Lesson learned: if your Edison don't want to boot, FIRST TRY: change your USB cable or attach a better power source!!!!