Yes, rendering is highly processor intensive, and it
is usually best not to have any other application
open or running while you are doing it.
I routinely have many applications running using iMovie and have never had rendering problems. Rendering isn't a time-sensitive task like importing video from the camera, so iMovie might render a tiny bit slower — although I've never noticed it — but it certainly shouldn't render any differently. Nor should it fail to render.
My guess is something else is causing the failure to render. Perhaps an issue affecting the disk, or third-party QuickTime or iMovie add-ons interfering with QuickTime, which iMovie relies on for many tasks.
http://discussions.apple.com/message.jspa?messageID=4176921#4176921
http://discussions.apple.com/message.jspa?messageID=4030731#4030731
mszig, the fact that you successfully used iMovie in the past doesn't mean everything is/was okay. Projects differ, and complications that arise with one may not arise with others. The trick is to find the cause of the problem and eliminate it.
You don't say exactly what went wrong when the project "stopped rendering". Rendering can refer to lots of different things. What exactly failed, and what type of clip(s) were you trying to render?
Karl