The Hauppauge cards are tuner cards at heart, not video capture cards. For the most part this is because none of the analog video systems (and Component Video is the best of those) comes close to the resolution and colour quality of current digital video systems. Thus, even if you have a way to convert, the resulting quality is only as good as the original analog system.
In fact, the Hauppauge cards CAN give you full HD digital TV signals IF those incoming signals are NOT "scrambled". Any current digital TV signal you pick up with an antenna from a nearby broadcasting transmitter will not be scrambled. That signal type is called ATSC, and that system of sending out digital TV is often called "OTA" of Over the Air. On Commercial cable TV distribution systems it is possible to have three types of TV signals. Older totally analog signals can be broadcast, usually on the lowest channels 2 through 13, for the convenience of people with only an old TV and no need to unscramble premium channels. Unscrambled digital TV can be broadcast with a system called Clear QAM. Then scrambled digital channels can be broadcast also, and those REQUIRE a decoder set-top box. Each cable TV provider makes their own decisions on what types of signals they will carry. Few carry analog any more. The Hauppauge cards' tuners can handle analog TV from OTA transmitters or on a cable system, plus digital Clear QAM unscrambled signals on any cable system. Not surprisingly they make no attempt to descramble the other channels and defeat the entire design of pay-for what-you watch. The original basic design for these cards was to tune in an analog TV signal and use its own dedicated processor to convert it to a standard digital file format that could be stored on a hard drive and reviewed later. With the advent of digital TV, the job is even easier because the incoming signal already is digitized in a standard format, so no real conversion is needed - the card can simply store it on the HDD.
But that only works for unscrambled signals.
These days when you contract for cable TV service most or all the channels are scrambled, and the set-top box you get from the provider has the way to decode them. Then the question is: in what form do they output those decoded signals to your TV or other equipment, both in terms of cabling systems and in terms of signal quality? Bear in mind that the cable TV operators are not the least bit interested in making it easy for you to snag their high-quality HD TV signals and capture them on a computer. They only want to sell you a way to WATCH the programs. Some will be happy to rent you an additional box, a PVR machine, that will work with the decoder to allow you to record some programs on it and watch them later. But even these boxes do not make it easy to take that recorded program and export it to another capture device.
So you have a set-top decoder box that must be used for any scrambled channel on your cable system, and that MAY be all of them. The only outputs it has are older analog systems for older TV equipment (not even including the best of these older systems), plus one HDTV output system, HDMI, which is almost universally available on modern digital TV sets. Actually, I have not seen anywhere in this discussion what real HD quality that Cisco box makes available on the HDMI output, but at least I expect it to be better than S-Video.
On the other hand, the Hauppauge cards never were designed to capture high-resolution video from other computer systems. So if you want to try to capture the digital video signals on an HDMI cable (plus audio) and have those converted to a standard computer file format for storage, you need a different capture card, not a general tuner card. I found some on one on-line retailer website by searching for Video Capture Card HDMI. Cards for PCI slots often don't have a HDMI output on them, so your feed from the decoder box can get to your computer, but not back to your TV, without some re-connecting. Some devices sold for capturing signals from your third-party gaming machine do have HDMI pass-though capability, but use USB connections to your computer and do not do well at compressing video to smaller files. Anyway, you can do your own search if you want that capability. Just remember that capturing, compressing and storing high quality HDTV is a demanding task requiring high-performance equipment.