I spent a while trying to find out about this yesterday evening but it all seems a bit confusing. As I understand it...
As things stand at the moment, it seems to be important to distinguish between a computer with internet connection and a computer with a TV/radio card:
Even now, a computer with TV/radio card should be registered and the fee paid where appropriate (see below though).
A computer with internet connection:
- until 31st Dec. 2006 -- no charge.
- from 1st Jan. 2007 -- should be registered and the fee paid where appropriate (see below).
However, in any one household only 1 TV and 1 radio actually have to be paid for. Any further radios (e.g. car radio) or TV's (and this presumably applies to the PC with TV/radio card and, as of 01.01.07, PC with internet connection) simply count as "supplementary devices" and are included in the 1 TV + 1 radio fee. (There are, however, more rules regarding other household members with an income above a certain level and additional TV's, radios, etc.)
So I think that whether the PC with internet connection will be "extra" or "included" will depend on whether you're already paying for TV + radio (which, let's face it, almost all of us
should be doing anyway...

) or not. So as I interpret it, as of 01.01.07:
- if you're paying for 1 TV + 1 radio (currently €17.03 monthly), your PC with internet connection won't cost you extra
- if you're paying for 1 TV only (currently €17.03 monthly), you should also register your PC with internet connection, but it won't cost you extra
- if you're paying for 1 radio only (currently €5.52 monthly), you should also register your PC with internet connection, and you'll have to pay the top-up fee for TV + radio.
I might be wrong though, and the usual disclaimer applies to this post...

Phew!