You are probably thinking of a PCI TV Card with TV Out - best known names include Hauppauge, Aver, Expert etc.
Best allrounder is a digital terrestial TV/Radio version (Freeview) such as the one I have, a Twinhan VisionPlus Ter; however it doesn't have TV out despite also being HDTV compatible, recording facilities, EPG, Preview etc...:-)
Some TV Out equipped alternatives include:
Reviews of some cards (plus using one with Linux):
Using such a long cable will probably degrade the signal to some extent - however, some TVs seem to have a higher sensitivity chassis and can handle weaker aerial inputs better.