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If one of precisely ten men, who form a minyan, had driven to shul (the synagogue) on shabbat, is that an acceptable minyan?
I would have though not, since one is benefiting from his melacha on shabbat, but was told that either this is not called a benefit, or that one is allowed to benefit from melacha that is done by a Jew on shabbat in general, just not in the case of bishul.
Are either of those two things true?
You certainly can't benefit from a melacha done by a Jew on Shabbos, not just bishul. Bishul is just the common, obvious example (see here for a source I could find online - where many different types of Malacha are a problem. It is talking about a non-Jew, but it is certainly not less for a Jew).
My first reaction is "מצות לאו להנות ניתנו" - Mitzvos are not given for benefit, so something which is forbidden to derive benefit from can still be used for a Mitzvah. Especially in this context, where the benefit is indirectly from the work (it is not a product of the work, like bishul, in the direct sense - like @Shalom alludes to). But it could entirely be about the benefit being indirect.
Cooking is a case where the food is a direct physical result of the prohibited action. Don't eat that food on shabbos.
Okay this fellow happened to have driven himself here, but he could have gotten here on foot or in a wheelchair (assuming eruv); I don't think counting him in for a minyan is the same type of tangible benefit from the direct result of prohibited labor.
A more interesting question: if I open a synagogue someplace where I know most people will drive, am I facilitating that? Rabbi Rakeffet discusses it and mentions the psak he's heard: if there are ten people within a two mile radius then it's conceivable to have a minyan without anyone driving, therefore it's permissible to open the synagogue.
