If the sketch waits for the USB port to be ready (Serial), it will get stuck in an infinite loop when there is no computer USB connection. Comment out the code and see if it will run. The ProMicro has a 32u4 microcontroller so the Serial port is native USB, not UART.
void setup()
{
...
while (!Serial);
...
}
If this does not help, post your code.
Update: ProMicro does not have a reset button so use a wire to connect RST to ground.