I've had the same problem with rendering some scenes, depending on how detailed it was, and how I chose the final render to display, and I only have 512MB of RAM. Most of the time, the renders took a bit longer, but I would get a final render that was pretty good.

However, if you are running on XP Pro, you might want to check in Windows Task Manager, and see what OTHER processes you are running, and close down the things that are not system critical (such as Quicktime), as these use system resources too.

Good luck