I'm afraid the idea of a one box live stream service isn't attainable at least if you are trying to host it yourself. The article you linked to from chris.kehayias.com is a good one and I have used that to build a Roku app. I think the best idea if you want to self host is to use Wowza media server
http://www.wowza.com/ (You can put this on your own Windows server if The perpetual license is $1000, but you can get a 20% discount because you are non-profit. You will also need a media encoder, you could use Adobe's one, but I would recommend Telestream Wirecast ($500, but non-profit discount also available
http://www.telestream.net/wirecast/). vailable). So you would have a box with say a Black Magic Decklink SDI
http://www.blackmagicdesign.com/products/decklink card in it running Windows 7 with Telestream Wirecast. This box encodes your video to H.264 and sends it to your server which runs Wowza Media Services. From Wowza, you can send out live video to nearly anything you want to including a Roku (HLS), Flash player (RTMP), and Apple IOS devices (HLS). You could replace the Windows media player streaming with something like JW Palyer (Free non-commercial use
http://www.longtailvideo.com/jw-player/) to play the live video in flash on your website. This is how our church is setup right now at least, and I am pretty happy with it. Altogether this system cost us around $2,500 for an encoder computer, the capture card, and all the software.
One other product that I have been interested in, but haven't tried is the Teradeck VidiU
http://www.teradek.com/pages/vidiu, it is a small box about the size of a Roku that replaces your encoder computer and cost $700, wich is cheaper that buying a PC, cards, and software. It supports sending out RTMP stream which could be pulled into Wowza.
You could also look into an account with Livestream.com or Ustream.com. They have free and paid options depending on how much content you want to put out and how much control you want to have, but they take a lot of work out of it for you.