Why wont my car start and why did the engine start smoking?

You know we can't see it over a computer so your going to have do the searching. A fuse link wire tapping off the larger starter terminal could have burned open. You could have a loose or corroded battery cable. Even a shorted starter is rare but possible.

The place to start is by measuring the battery voltage with an inexpensive digital voltmeter. If you find 12.6 volts, the battery is fully charged. If you find around 12.0 volts, it's okay but discharged. At 11 volts suspect a shorted cell and the battery must be replaced. If you find 0 or real low voltage, something is shorting it out and you'll just damage another battery and possibly cause an explosion when trying to connect it or jumper cables.

If you do find 12.6 volts, turn on the head lights, (even if they don't work), to draw some current, then measure the battery voltage again. Now move the meter probes further down the line to see where the voltage is lost. Move the negative probe from the battery's negative cable to a paint-free point on the body, then to the engine. You should still have 12.6 volts at those places. (If the smaller black cable bolted to the body looks like the insulation melted or overheated, the larger black cable bolted to the engine has a bad connection).

Next, move the red probe from the battery's positive cable to the large terminal on the starter. You should have full 12.6 volts there too.