I finally got it working properly:
my two home theatre PC's (HTPC). One upstairs, one downstairs.
Until yesterday, the 'real' TV's image got blurred as soon as I turned one of the HTPC's on. And the one upstairs had never shown a clear image.
My guess that I needed to really split the cable signal and boost it with a Hirschmann amplifier turned out to be correct.
So 150 Euro and some tinkering with high quality Coax cable later it all works.
Downstairs I built two digital TV decoders (from FireDTV) into a Windows machine, so I can watch and record digital TV. Windows Media Center still doesn't understand high definition TV (streaming h.264 to be precise) so I'm using software called DVB-Viewer together with CoreAVC to watch and record the three High Definition channels on my cable.
Upstairs is a more traditional setup with a dual analog tuner built into a Windows Media Center PC.
Ironically I hardly ever watch TV, but hey, I'm an innovator so I did it just for fun.
Next up: streaming live TV wirelessly from my HTPC to my MacBook.