At a glance, I see two things wrong with your setup:
The enable input is inverted (it is actually [o]ENABLE[/o]), meaning that the motor outputs are disabled when that pin is driven high, so it should be set to logic low for normal operation. It has an internal pull-down resistor, so you can leave it disconnected if you do not need to change the pin’s state.
The [o]RESET[/o] pin needs to be high for the outputs to work. You can connect it to the adjacent [o]SLEEP[/o] pin, which has an internal pull-up, to pull it high.
We have a minimal wiring diagram on the product page for the A4983 driver carrier that you can use to check your connections. Please let us know if you get the driver working.