You would need a videocard, yes; however, you'd be very limited by two things:
1- the power supply. That system (according to the page you linked to) came with but a 200W PSU. A decent card will require a 300-400W (minimum) PSU.
2- the PCI bus. Even a card built on a good chip (such as an HD4350, or a 9500GT) is so strangled by being on the PCI bus that it just can't do what you want.
Case in point: ATI actually disables hardware acceleration (which you need for Bluray playback) on the HD4350-based PCI cards. Reason: the bus just can't handle the datarate required.
Tuners:
Actually, you'd need a card that supports Clear-QAM. ATSC is over-the-air digital, QAM is digital cable.
Also note that Media Center, prior to the TV Pack 2008 for Windows Vista, does not natively support Clear-QAM (TVP and Win7 do.) For 'older' versions, you'll need to go with a tuner who's manufacturer has created a 'virtual-ATSC' driver (allows a QAM tuner to be seen as an ATSC tuner, allowing it to work.) Avermedia, Hauppauge, and SiliconDust have done this.
Point #2: if you're running Media Center 2002-2004, you don't even have ATSC support. MC didn't get that until Rollup 1 (or, was it RU2?) for Media Center 2005.
If you were to upgrade the box:
$80 for an HD4350 PCI (which can't do Bluray, and will even struggle with HDTV playback), and you're getting a card that you cannot recycle into a newer PC;
$70 for a good PSU.
That $150 is a good way toward building a new PC, that actually can do what you want. I have a sample build on NewEgg, based on a Core i3, that's just under $500:
https://secure.newegg.com/WishList/MySavedWishDetail.aspx?ID=13696186
(note: viewing wishlists on NewEgg requires logging in to the site. If you don't have an account, you'll need to create one.)
$500 will get you a new machine that can do hi-def (and Bluray) playback, and is actually upgradable.
Just a thought....
~Chris
'nearly every day of my life is some kind of computer hell'
Desktop: E7300 on GA-P31, 2GB, HVR-1250, HVR-2250, ATI DCT (internal), HD4650, Win7 Pro x86.
Server: Intel E6400, GA-965G, 4GB, 2x 500GB WD, 2x NV DualTV, 3xHDHR (2 QAM, 1 ATSC), HD3650; 2x Xbox360; Win7 Ultimate x64