If your system doesn't meet Final Cut's minimum requirements, then there's not a whole lot you can do about it without pulling out a credit card.
I have one of those Macs ? identical to yours, in fact ? in my closet right now. I ran Final Cut on it extensively, but I don't recall what version. It was a fine machine for doing SD work; I wouldn't consider trying to do HD on it, personally.
Maybe you could find a Quartz Extreme-compatible graphics card upgrade for it?