Gadict:
Yes, but I changed the code a bit, so it would send 100 to the motorPin, instead of reading from the serial monitor.
That wouldn't cause any problems. The motor in the kit can pull more power than the Arduino can supply directly, which is the need for the transistor and diode, as explained in the training material. So, as long as it's wired up exactly like in the picture, the Arduino should be 'protected' from excessive current draw from the motor. You're essentially building a simple electronic speed controller.
This setup should not be capable of burning out the Arduino, but it sure does sound as if yours might be bricked. IMO, that should not happen, so if you're sure you wired it up correctly, I would call the company you got the kit from, and see if they might replace it for you. They may also know of a trick to revive it. Check your wiring real carefully before doing that though.