Today I had business in the suburb, Glostrup, where we have a "BilTema" shop. They har the right distributor cap for 39.90 DKr. Which is about €5.
With the new cap the car started immediately. Which makes me wonder how long the cap has been going bad. The spare I had tried first did have some carbon center pin sticking out, but apparently not enough to reach the rotor. Both old caps are now in the trash.
So if your car is difficult to start. Check that the centre pin is long enough to reach the rotor.
I took a picture of the replacement cap I had on hand and which didn't work either. As you can see in the photo 6-7 mm of the center pin was still sticking out and had proper spring load. But it apparently was not long enough to reach the rotor.
The new cap has about 1.5 cm pin sticking out. Alas I was too anxious to replace it so I forgot to take a picture of that.