Ok, finally found the time to do more investigations.
I put the Xonar card in the 16x slot and there was no issue. The sound played fine.
I tried the graphics card in the old PC, just to be sure I hadn't damaged it. Again, all was fine.
This time I tried booting without the Xonar card installed - however, no go, monitor still refused to turn on.
I have to conclude, that this motherboard does not like my graphics card. There is no other explanation.