I suggest Amiga UNIX!
Kidding. Another vote for Ubuntu here. I typically run Debian on everything, and I like it a lot, but it can be frustrating for new users.
I recently set up a media PC with Ubuntu. It boots off the network into a Gnome desktop...completely silent! Reason I mention it was your TV watching, since that is one of the things I use it for (along with video files). Would
MythTV be what you were referring to? It says it has closed caption support. There are precompiled packages for it in Ubuntu in the multiverse/universe repository (forget which). I've got the backend component running on the mutant Debian fileserver, only the frontend in the living room. I use it to watch over-the-air HD broadcasts :-D I took a pic from when I was testing it on the fileserver
here. It is capable of running windowed, but I couldn't tell you how as I always want it full screen...it's "full screen" in the pic, it's just two displays.
If you're after something requiring less effort to setup than MythTV maybe you would like
tvtime.