I picked up a Lenovo y530 for 499 to do just that. It has enough cpu, ram, and HDMI to get it done. Maybe there's cheaper but look at the y530 as a benchmark on what it takes.
I have chosen to eliminate cable due to the availability of web-content provided by websites such as ESPN3.com, Hulu.com, and the network tv websites. I currently have an extremely old PC (2003) hooked up to our main television, and although the internet connection is typically sufficient to stream content, the computer cannot perform quick enough to meet our expectations. I don't know much about hardware but I would imagine that it is a result of a poor graphics card and slow processor.
I'm trying to purchase the cheapest PC possible, and the ONLY thing it will do is stream live video content from websites. Can anyone provide me with any suggestions as to what I need to look for in a PC, any suggestions, etc? Thanks very much for your help!