I actually have exactly that setup (shitty Gateway with Turion and 5400 rpm hdd, dirt cheap).
It works well enough for what I need it to do - surf the web, Office, Facebook, Youtube, Plants vs Zombies, movies, - heck it has an HDMI port. And I've been able to do some light programming on it without trouble.
Only thing it really doesn't do is non-casual games.
You're overestimating what most people do with their computers