Try manually resetting the board:
- Before uploading, run Verify.
- Hold the reset button and click Upload.
- Release the reset button.
If that worked, your board's reset isn't fried, it just isn't receiving a reset via the serial cable. If it failed, either part of the board or MCU may be damaged; something attached to the board may be inhibiting the reset signal; or the software may have disabled the board's reset pin. In the latter case, see the Arduino StackExchange article, How do I repurpose Arduino's reset button, for how this can happen and how to undo it if it has.
Is here anything wrong with using pins 12 and 13?
I'm not familiar with stepper driver, but at a quick glance at its data sheet, and it's logic being 3.3v & 5 v compatible, I don't see any problem with connecting any of its logic to any of Arduino's logic pins (almost all of them). Since the driver also has a motor drive-voltage input for driving your motors, accidentally connecting an Arduino pin to a driver pin (or anything else) carrying the drive-voltage could - probably would - damage at least the connected pin driver in the MCU, and possibly other parts of it as well.
If your Arduino has a socketed Atmega chip, and since you already know another Arduino works as you expect it to, replacing the Atmega chip will be the quickest, cheapest & easiest fix. Just go over your wiring and make sure no motor drive voltages are connected to the Arduino board.