You're going to need a capture card capable of HD recording. To my knowledge, most of those HD PVR cards are only good at recording from unencrypted coaxial input, be it cable QAM or ATSC from antenna.
For this reason, most people simply record a downconverted standard definition signal (SD, standard def), over the s-video, into a traditional capture card or DVD recorder.
HD is only transmitted over component or HDMI, so you'd have to get a card capable of that.
The Blackmagic card comes to mind, and has become
VERY popular in the past 4-5 months. It really snuck up on people, much how the ATI All In Wonder AGP Radeon cards did back in 2001-2002.
You're looking at about $250 total -- really good price, to be honest. The ATI setup was $300+ when it came out. This is one of the lowest-cost options for HD capturing.
You'll also want a really powerful computer -- a dual-core at minimum, but a quad-core would be better.
In terms of component vs HDMI -- it's not an easy answer of "HDMI is better". Indeed, there are MANY instances where component gives a more visually appealing picture. All things considered, there's not that big of a difference. HDMI/DVI often just shows more of the digital pixel noise than anything else. As is the case with other connector/wire types, not all connectors and wires are made equal. A really good component port/cable will easily surpass a cheap and crappy HDMI port/cable. Use what looks best because it looks best -- not because it's the accepted dogma of a self-proclaimed video purist!
Hope that helps.