The way to say 'My car doesn't start' in Spanish is the following:
'Mi coche no arranca'
The vocabulary that we use is the following:
Mi: (pronoun) My
coche: (noun) car
no: (adverb) no, doesn not
arranca: (verb) to start
If you are in Spain the word for 'car' is 'coche' but in other countries of Latin America you should use 'carro' or 'auto'.