The shutter of the lens works, when it's not mounted. I tried it several times this morning manually. The battery has 5.5V - 5.7V left, should be OK I think..
So the lens on its own works and the camera on its own works (with other lenses). I'll try cleaning all the contacts when I'm back home and see if the problem is there.
The cable release socket shows no red stripe. Only, of course, when the cable release is attached. I'll also try the cable release tonight, I didn't do that yet.