I now have a discovered a procedure in getting my DisplayLink graphic adapter working:
1: Shut down the pc.
2: Switch of the monitor connected to the adapter
3: Plug in the adapter.
4: Boot up, and wait till everything has started up.
5: Plug in the monitor.
It works most of the times. Pretty annoying routine, none the less.
This also means, that whenever the notebook is "put to sleep" or restarted, the process must be run again