How to stream the analog tv automatically (no X, and without VLC) in the house?

I have an analog tv card, and would like to stream it on other machines. This pc has no screen, and a big cpu, hence it could stream the channel played to all house (other pc's)

With what can I do that thing with Linux ?
the startup script is launched with inittab

MythTV is probably your best bet. You can setup the system with the capture card as a backend server, and the PCs you want to stream to as frontends. The frontends will likely need X, but the backend shouldn't (I don't think anyway).

You may want to look at the vlc-nox (that's No X, not nox) package. MPlayer also can run without X if you use the fbdev video output driver (-vo fbdev), but I think VLC is more capable when it comes to streaming from a capture card.

I've never used MythTV or fiddled with watching video on a framebuffer so I won't comment further.