Streaming Sky around really becomes the feature you wanna ditch. It IS possible, but generally becomes such a hassle it's not worth it. I *have* done it at work actually, so I can tell you how I did it to give you an idea of scope.
Hardware:
*Core 2 Duo/1gb ram/500gb) machine ($800ish at the time)
*Canopus ADV55 DV Capture box - this has RCA and S-Video on one side, and firewire on the other, and automagically converts the analog output from the Sky decoder into pure DV video. Computer just sees DV video coming in and runs with it. ($150ish maybe?)
Software:
*Windows 2003 Server (Host OS, required for Streaming Media Services US$1k retail)
*Windows Media Encoder (Can actually run on any machine, free)
*Windows Streaming Media Service
Encoder captures the DV stream from the Canopus box and converts it to whatever WMV format/spec I configured. I left this at DV quality. Streaming Media Service grabs that stream and broadcasts it across the network on demand. I left it at "broadcast" quality and tested it by opening the stream on every computer on the network I could at once (70ish) and it worked brilliantly, with less than 20% network bandwidth utilised (2 gigabit backbone, mostly 100mbit clients). Hell I was able to dial down the quality and stream it out of the network and watch it at home.
Pros:
*Was REALLY reliable. Never crapped out once.
Cons:
*Cost of hardware/software for the home user (in our case, we have free Windows licences, and were dropping $30k on a media suite, so an extra $1k was no big deal)
*Setup hurdles if not familiar with Windows Server concepts (in saying that, it was pretty straightforward as far as these things go, I had streaming working within 10 mins of looking at it for the very first time)
*You can't change the channel remotely
*Every client watches the same channel
*Only SD
Looking at it today for the home user, I'd try it with something like MediaPortal TV server or MythTV, although they are harder to setup and less reliable, and I don't know if they actually support DV in. That Canopus box is fucking awesome though. I would still use a dedicated server box.
The reason I suggest an embedded box like the Western Digital is they are reliable, play every format I threw at them, and are simple to use. Don't under estimate that last bit. A PC driving it still has a few pain in the arse things about it. A simple remote with a simple menu passes what we like to call the "wife test". Oh, and they run silent too, which a PC doesn't. The "PRESS BUTTAN SEE VIDEO" model is invaluable.
Doing it legally with budget? I'd totally use Apple TV's wherever I wanted a client, and a US iTunes store account. Because it then becomes SO fucking easy.