I just soldered my motor driver and Arduino together to a 12V DC power supply in parallel. This was just simplifying it down from having some leads tap into the power supply directly, so that there was just one barrel jack to plug in.
I'm using a 1.5 stepper motor.
The previous setup worked fine, and I had tested it multiple times with success. When I changed it, I tested the motor for a few seconds and turned it off. When I tried again a little bit later, the motor didn't move. I realized the board's light was off, but the motor driver's was on. As I was unplugging the barrel jack, the through holes were pretty hot---not solder-melting hot, but still very hot.
The USB cable is fine, and the red light will turn on for only a millisecond after plugging in, but the Uno is missing from the Port list and I can't upload anything to it, even though the "Arduino Uno" is in bold.
Heat is not good. Save your PC and buy a new Arduino.
If the Board/Port dropdown does not show the port, and Device manager does not show a device on ports >> comm/lpt, and your system does not chime when the USB is inserted... it is probably dead. The board is your's for testing your troubleshooting and soldering skills.