'Have' is only an auxiliary verb when it's used with a verb in a perfect tense (present perfect, past perfect etc.).
Ex.
Do you have a...
Have you done...
I had a...
I had done...
Actually, there ARE sometimes exceptions to this rule, but they sound old-fashioned.
So "I hadn't a car" isn't technically incorrect, but it's extremely old-fashioned.
"I didn't have a car" is the standard way to say it.