Humm.. I haven't seen many PC tuner cards that have any kinds of video outputs whatsoever. They may exist, but especially for HDTV units intended for PCs that is pretty unlikely since they receive digital video and have no reason to convert the digital to analog, and, in fact, they may use your PC CPU to do part of the decoding.
If you have a GPU card with SVIDEO out like many NVIDIA or ATI ones you can conceivably capture the video with an HDTV card/tuner/usb tuner, decode it / play it "on screen" and pipe the screen output from your GPU card that is playing the video out to the GPU's integrated S-Video port. That option may not work well or at all if the content is DRM protected though.
As for cable + HDTV tuners, you will NOT EVER (in the current state of affairs) be able to tune premium, encrypted, pay per view type channels with a PC based tuner / card, it just isn't possible. They don't LET the PCs decrypt the signal even IF you're paying for the cable access to those same chanels! The only way to decrypt them is with a compatible cable box tuned to your subscriber code.
Technically they do sell a "cable card" setup which is PC based that can decode most of the encrypted / premium channels (video on demand / pay per view may still be problematic), but you can't just BUY a cable card to do that. You have to buy the WHOLE pre-assembled integrated PC, and then you can't really customize / upgrade it. So really it is just an expensive cable box with a few outdated PC capabilities that they might be nice enough to sort of let you use.
Now many HDTV tuners for the PC CAN receive "clear QAM" signals from cable systems as well as the "over the air" free ATSC HDTV / digital TV broadcasts. However the "clear" part of "clear QAM" means you'll only get the freebie, unencrypted cable channels, which, usually are pretty much limited to free broadcasts from your local over-the-air TV stations and so on.
check out "the green button" site for info on Vista / XP "Media Center" and its capabilities for this sort of thing.
mythtv is a good LINUX based DVR (think Tivo) system.