I noticed that the ASMedia 1061 was listed in the device manager as "Standard SATA-AHCI Controller"* under the tab "IDE ATA/ATAPI Controller"*. After installing the driver for the ASMedia, I find the controller correctly under "Storage Controller"* and can install iCue without freezing the PC during installation.
I took the driver for asm106x 3.2.3. Unfortunately I did not find any official sources for the driver and downloaded it from station-drivers.com.
* (I use a German Windows and am not 100% sure about the terms.)
Thank you very much, feisty, I had to remove the devices (LiteOn Bluray, Seagate HDD) from the ASMedia ports and it worked. The problems are definitely related to the ASMedia controllers. Unbelievable...