Does the sentence contain faulty parallel structure?
The mechanic told me that I would have to decide if I wanted to have the carburetor fixed or if I wanted to buy a new car.

The problem with this sentence is the words "if" and "decide."

It should read "The mechanic told me I would have to choose whether

I wanted to have the carburetor fixed or I wanted a new car," or "  

.. choose between having or buying a new car."

alright, that is a bet.