Thanks for your help, nForce. I'll try to identify the model for you, but it doesn't seem to be anywhere on the box that the card came in. The card itself has a tag that says the P/N (product number, I assume) is 102B3830200 218432. The packaging describes the card as an All-in-Wonder HD, 512MB, PCI Express 2.0, HDTV Personal Video Recorder, Full-HD 1080p Video Playback, DirectX 10.1 Support, HDMI with 5.1 Surround Sound, Powered by ATI Radeon HD Premium.
I want the following configuration: One of my two computer monitors will act as my main Windows display. The second computer monitor will be an extended Windows desktop and will be cloned to an HDTV monitor. The first ATI card will power the main Windows display; the second card will power the extended Windows desktop and the HDTV monitor.
I don't know whether I actually need a crossfire connector, because I don't know enough about the technology to understand what purpose it would serve. Can't I just run my configuration with two cards in separate slots?