Ouch! I think you've put mains voltage into your Duet. It's unlikely that much has survived. I guess there is a chance that the bown stepper drivers have protected the rest.
If you have access to SMD hot air equipment, then you could remove all the stepper drivers, as they are obviously blown and may be shorting out the 3.3V supply. The apply USB power, and see whether the red 5V and green 3.3V LEDs light up. If they do, but the Duet doesn't appear as a USB device to the PC, try putting a jumper over the Erase pins ands press Reset, then see if the Bossa port appears on the PC.