http://www.billag.com/web/de/fragen_...en/geraet.html (German) tells you that with a device capable of receiving TV programmes, you must pay their fee. Ditto for radio reception....

So:
2G/3G phones that can get TV/radio
Computer that can download and play programmes from the internet (as well as TV tuner cards)

are included amongst the "obvious" TV and radio devices (including those, for example, in a car).

To get out of paying you must have a device that has been crippled from being able to play back TV programmes:

Wenn das Gerät technisch in der Lage ist, Programme zu empfangen, sind Sie melde- und gebührenpflichtig. Es reicht nicht, die Antenne abzuhängen oder das Gerät nicht an das Kabelnetz anzuschliessen. Nur wenn keinerlei funktionierende Antenneninfrastruktur (Satellitenspiegel, Zimmerantenne oder Kabelnetzanschluss) vorhanden ist, besteht für das Fernsehgerät keine Meldepflicht.

So the issue is that you have to ensure it can't connect and receive programmes. Given that connecting it to a DVD or VCR means that you can playback recorded TV programming to me creates a caveat that you can either get away with or they can make you pay.