Then the computer with the MSI board with a new box with an ASRock Z77 Pro4 was replaced - and the problems went. Because apparently, after switching on the power strip (the computer is not at this time of) where no current to the USB ports. This means that after starting the computer, neither an image is displayed even mouse / keyboard work. This could be solved with a workaround by advance the socket of the other computer (the ASUS board) has been turned on.
Now that I have the computer with the ASUS board replaced last week (by the completely same configuration as the first computer with ASROCK Board), the switch is no longer usable because it loses power after turning on the power strips. I must now be either both units permanently at the current or after switching on the power strip off all four USB connections to the switch and plug it back in. Then the current is as miraculously back. So the device is, however, no longer usable for me.
The support of Aten responded to all my requests within two hours (very good!) But could not offer me any solution. So I can unfortunately only the KVM switch with 3 stars Rate (at the beginning of use, it would have been 5). I will now look for another switch - ideally with its own power supply.
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Addendum: I could the problem of power supply in the meantime dissolve itself after the support also no longer knew me and recommended only the use of an expensive switch with external power supply. The black USB ports are not as described in the manual charge of the mouse, but only for the power supply. Therefore, I have a black USB ports plugged into a powered USB hub, which hangs permanently on power - and lo and behold: the KVM switch has power immediately and will work again just like at the beginning. On the score for the product but that changes nothing in my eyes, because I had to even take care of a solution and even inserting additional hardware.