I solved the problem!
In the event viewer I found 2 errors regarding the IAStorDataMgrSvc. The first one stated:
IAStorUtil.StorageAction.VolumeCreate action failed: FailedToClaimDisks
Feeding google with it results in only 2 hits (now it might be three ). The first one helped me out. It was the antivirus software ESET, which caused the trouble. Only deactivating it wouldn't help. I really had to remove it temporarely. Now it works!