Have found Charon Frigates that appear to be movement-frozen; they can still shoot back, but will NOT move under any circumstances.

AFAIk I was running unmodded at the time.

I think that's supposed to happen with some frigates as they sit near Korolov routes waiting for their prey. They usually don't move until you finish the escort mission you were doing, and even then they'll sit around for a while. But if it sat there after you did several missions, attacked it repeatedly, etc... then I guess its engines were broken.