The short legal answer (presuming you are subject to US law) is: yes, you will require new kit. I don't know how many CRTs actually supported HDCP, and the cards you mention probably do not as well (HDCP requires every link in the chain to be compliant) -- well, perhaps the 7800 GS. You'll need to look at the exact manufacturer specs to learn if a card supports HDCP. Especially during the transitional period, it wasn't uncommon for two models of the same card (let's say the Radeon X1600) to differ on HDCP compliance.
If any link does not pass HDCP, then you might get an error or a downscaled image (less than 720p).
Realistically, what this means for punters stuck with older kit, is that they'll watch their desired content in an extra-legal fashion, and Hollywood will have lost another customer to oppressive DRM. DRM ultimately hurts only those who are trying to take the legal route.
There are of course applications that will strip DRM, some of them in real time (ie as you view), but their discussion here is likely verboten.
Facebook
Twitter