Define "fun" games. Cuz I hold Blue Dragon and Lost Odyssey in high esteem, but they're fairly traditional JRPG flair, and lots of folks don't consider those fun. These are two great games, though. ^_^
Midnight Club, Forza, and Need for Speed games are almost always Goodtimescity. Too Human is good stuff that got a bad rap for some reason. It's great cyber-myth with fun action-RPG combat. Phantasy Star Universe is cheap and good stuff, but you'll have to pay a subscription fee to play online. Offline is still fun and good stuff, though.
Mirror's Edge. So good. It wasn't as popular (with the press or public) as it should have been. It's great. Just remember that it isn't a shooter, so don't try to play it like one (most complaints were about the shooting mechanics, I believe... but I maintain that it'd be silly for a free runner to have the gun skills of a specops soldier, so I wasn't bothered by it; I even played the whole game without ever shooting anyone!).
If you missed any of the old BioWare games (Knights of the Old Republic and Jade Empire), they're cheap and greatness, too.
That said, I wouldn't rule out PC games due to your hardware unless you just don't like gaming on your computer. There are a plethora of older games (and current indie games with lower requirements) that you may have missed that should run fine on your machine. Games that are exceptional.