You can much more bang for your buck using specialised chips for handling video than a high end general purpose CPU.  This might be in a better camera, a better video card, or an external encoder device.

   You can get an external encoder that plugs into usb and uses specialized chips to encode the data.  http://www.cwol.com/ipod-ac cessories/instant-video-to- go-ads.htm

    Also, depending on the software you use (like the latest Adobe products), getting a high end video card for $200 or $300 will allow it to use the graphics chips to speed up encoding a lot. 

   Also, for any encoding, it will be faster if your source file is on a different physical disk than the destination drive.  If you have to, output to a fast USB drive, but the best method is one SATA drive to another.

   Another thing to look at is to get a camera that produces the video type you want in the first place.  You can often get a camera that has analog RCA or SVHS out as well as storing data internally.  You could use the RCA for live streaming while storing the video internally in your desired h.264 format. 

   It would help if you told people as much as possible about the chain of formats that you currently use.  What format does the camera capture initially?  What format or method is used for live streaming?  What software do you use for video conversion? Do you need to make files with 2 or 3 different formats?

  You should also try to make this a computer that never goes on the internet so you can turn off anti-virus programs that slow everything else down. Try getting a KVM (keyboard video mouse) switch so that one person can control this computer (off the internet) and their main computer (on the internet) with the same monitor and keyboard and mouse.  Also, get rid of as many background programs like Real on the encoding computer.

   Also - I notice you sometimes line up a youtube clip and it isn't available any more.  You can download youtube clips using firefox and the addon "DownloadHelper" and play it with the free VLC media player (get VLC free at download.com, which is owned by the CBS network, so it is safe)