I don't have a Dutch etymological dictionary here, and the online one requires a license.
"Pech" in Dutch ("pekh") in general means bad luck, yes, usually in not so serious contexts. Something like "too bad" or "bummer!".
In the car context, although no doubt the word was originally used to mean bad luck, by now it really means breakdown, as you say, specifically while en route**. (If you can't start your car in the morning, that's not pech. If your car breaks down while on the highway, that's autopech.)
How about impedicāre (to trap, to entangle), the root of impeach and impede (hinder, prevent), and related to empêcher?
**There's something pleonastic about "while en route", but it seems like the "en" in the English form doesn't entirely capture the "while" aspect. Any opinions?