I'm running on an AMD A8 Quadcore clocked at 1.9 Ghz, in an HP Pavilion G7-2341. It would have only cost me 400 bucks, but I got to pay only $350 for buying the floor model.
It is cheap and effective. The discrete-graphics work great in PS2. I can actually run with very playable FPS at Low/Medium graphics; around 30 or 40 FPS unless I'm in a big fight. If I'm careful and pick my fights,
I can run on full Ultra at ~20-30 FPS. Even then, the FPS is smooth with no input lag.
HP Turbo Boost is how I'm able to play. It automatically overclocks your processor when you switch to the High-Performance power mode. Razer GameBooster also comes with a power-mode that automatically applies when you run it on a laptop. I run PS2 at around 2.4 Ghz, on a card that normally only runs 1.9 Ghz maximum. And when you switch the power mode back, it automatically re-clocks to 1.9 Ghz.
Between this Turbo-Boost tech and the HP CoolSense feature that comes built-in, my laptop won't ever have a chance to overheat. But just to be safe, I bought a $10 dock that runs a cooling fan underneath the chassis. It works like a dream and it's pretty sturdy.
All in all? There are plenty of options for people to play PS2 that can't afford a Falcon Northwest, high-end ASUS or IBuyPower laptop. Or even.. Alienware.
You just have to look for it.
I'm more than willing to help out with anyone who needs to find a cheap comp that can run this.
enjoy.