"The clock does not have a battery."
Translation:El reloj no tiene batería.
That would mean it doesn't have "one" battery, which means it could have two, or three, or a dozen :)
If you wanted to use an article here, you could, but the proper one to use would be "ninguna".
In Spain the word pila is usually used for small batteries. Mobile phone batteries are called baterias though.
Yes, it's pretty common to hear things like «mi teléfono no tiene batería», meaning that the phone's battery has no charge.
Why was 'tengo' incorrect? Is that used for I have... instead of it has...
In english we can say the clock has no battery OR the clock doesn't have a battery. We have the option of saying this sentence the second way using the "a". In spanish there is no option to say it the second way using "una"