[Mathias]

Batteries don't go as low as 10V without reason, so you got either dead battery, dead alternator, or current leak. If you're still on the original battery I'd wager that's the failing item, which would be the best of the alternatives as it's easy+cheap to fix.

You haven't noticed cranking being slower/longer than usual lately? My battery went the other week but showed signs long before actually giving up.