Easy Fix to this rather than a huge Hodge Podge of Cables to accomplish what your doing. You have several Options now days Some more expensive that others.
1st question ya gotta ask do you want HD or SD Video. Im Guessing SD since most play tube TV's or those 19in Viewsonics.
Next questions are you using Component or Composite video..
For Most SD video you can get an Old ATI All In wonder it has an external Cable that allows for Video in with a Loop feed back out. You can round one up for about 30 to 50 bucks Caveat is that you will need a Mobo that supports AGP.
Next Choice this is assuming you want HD or SD and do Not want to stream your video live. Buy you a Cheap 99$ DVD Recorder. Works just like a VCR would. the HD versions are a little more.
Sling Box.. Yes.. Sling Box.. Hook that puppy up just like you'd hook it to your cable box. And with your sling account you can stream that to the net. Not sure on who all can watch it though? But Theoretically you should be able to use a sling box. the small standard one runs about 130ish.
If you want HD, follow this Link its your best option
http://goodblimey.com/archives/2008/02/06/how-to-record-xbox-360-gameplay-videos/ its not cheap though the HAVA is pricey buts its good quality it works alot like the slingbox does but does not require a slingbox account.
Here is another way i Saw.. Its a Cheap Hodge Podge way.. uses s-video.. which I personally think is horrible quality.

Also here is a GREAT blog post I found on a how to
http://kobo.isgre.at/2009/07/01/what-do-i-need-to-record-off-the-tv/Lays it all out for ya. If it where me though? And I didnt have the requirement to Stream live.. Id be buying me a DVD Recorder and your done. You just set that bad boy up just like the golden days of VCR's XBOX 360 > DVD Recorder > TV Bam. Instant Recording with no Hodge Podge. and No Computers to have to lug around with ya. Bam here ya Go PERFECTION
http://www.google.com/products/catalog?hl=all&q=DVD+Recorder&cid=18190521838058060869&os=tech-specs#pThat will do Old Technology Cable Connections, and New Style HDMI and records it all as DIVx and it support Dual Layer if you go full HD Recording. And if you really wanted to stream it just put a "Amplified" Splitter in-between the DVD Recorder and the TV and bring a Laptop with ya and a cheap ole USB Video In Adapter you can get those for like 20 bucks. and just use it to stream it to the net. you dont need good quality when you stream it anyways since you need to compress it and make it as small as possible so it dont jerk every 10 seconds. I Recommended
www.qik.com or
www.seesmic.com both are equipt for the need and they will publish to Facebook and MySpace and they are free. Or Use a Jailbroken iphone with the Qik.com app on it. and Just have your iPhone Stream it like someone would with a camcorder.
Lots of options.. Dont kill yourself with a PC / Tons of Cables Be a Minimalist and still get the same things accomplished.