Here's my rig that probably wouldn't run Turning Point. The case is about 10 years old but all the bits are a bit newer than that, they've been upgraded over the past couple of years here and there.
It's an AMD 2.8Ghz something or other, with a GeForce 7600 GT and 3GB of RAM. It's done me pretty well over the years, and runs extremely smoothly for all the crap that's installed on it. It's running XP, of course, Vista would run like a dog with three legs.
Hopefully I can have it replaced with that beast of a machine Dtoid is giving away, which of course is the reason for this post.