If an auto repair shop runs two diagnostics, finds basically nothing, and tells me to take my car elsewhere, do I still have to pay?

On New Year’s Eve, my car decided that it would not start. I have had this problem once before, and it was an electrical issue. In response, I had AAA tow it to the nearest large auto repair shop (Firestone in this case) because they would be most likely to have the parts necessary to fix it.

Anyway, they ran an electrical diagnostic, found nothing, then a compression test, and found that the engine was flooded out with gasoline, but do not have the capability to find out what had caused that or if that was even the reason why it would not start. So they said I have to take the car somewhere else. My bill for this valuable information is around $130, and it still won’t start, so I have to tow it AGAIN.

I called the other mechanic I’m taking this car to, and he could not figure out for the life of him what in the world these other mechanics had even tried to tell me.

What I want to know is whether I can raise enough of a fuss in order to not have to pay Firestone the full cost for these useless diagnostic tests, what the heck I am supposed to do now, and whether this would constitute justifiable assault and battery.

And fyi, the car is a 1994 Volvo 960.