Hey Hattie -
I'm a pretty avid PC gamer and I've built my own machines for years. I've also accumulated far more knowledge than I ever wished I had regarding tweaking PCs for video performance.
The most important aspect of your PC as it relates to gaming/video performance is the video card itself, followed closely by your CPU and RAM.
300Evil already posted the game specs.
Your PC's specs are here:
http://h10025.www1.hp.com/ewfrf/wc/document?lc=en&cc=us&dlc=en&product=213890&lang=en&docname=c00009592
Your PC uses integrated video - that is, the video is run off the motherboard itself, rather than with a separate video card.
This is your problem and this is why the graphics are stuttering. The onboard video (Integrated Intel AGP Graphics with up to 11MB dynamically) isn't powerful enough to render the graphics properly, simple as that. Upgrading RAM is a waste of money.
Also - it appears your mobo doesn't have an AGP slot, there are only two free PCI slots (not to be confused with PCI-e).
So you could try bypassing the onboard video and buy a cheap used PCI video card, but again, it's kind of a waste of money. PC graphics have advanced so far so fast that even AGP is quickly on the way out. Video cards have gone from PCI (yours) > AGP > PCI-e. So getting a decent old PCI card may be tricky and more importantly - drivers and support for those cards will be archived and out of date.
Bottom line is your machine wasn't really designed for running games and isn't really customizable. Even a low-spec game like this one will have trouble running on it properly. If you're going to be doing any more gaming at all, I'd get a newer used machine with better specs and upgrading capability. Look for a machine with an 8X AGP slot (or even better, PCI-e) and DDR RAM on the mobo.
You could try throwing some more SD RAM into your machine (it's cheap) but I really don't think that's going to help much, if at all. Lol..I've got stacks of used SD RAM, I could mail you a few 128 MB modules if you want for free!
EDIT: Just noticed your mobo only has a total of two DIMM slots, for a total of 512 MB. So you'd need two separate 256 MB SDRAM modules to get your max memory, which at 512 MB of SD RAM, isn't going to cut it.
If you need any more help, just let me know!
C.