moracca:
I don't mean to beat a dead horse here, but I was hoping someone could explain why I don't have these problems when the arduino is powered by my computer's USB port?
Your computer will supply at least 500mA, possibly 1A of current. A 9v might supply a couple hundred mA for only a few seconds before falling flat on it's face.
I am not sure which went first, the 9 volt battery, or the onboard 5 volt regulator.
If you are using the PC usb, the onboard 5 volt regulator is not being used.
When you connect the 9 volts to the Vin, the onboard 5 volt regulator has to drop that 9 volts down to 5 volts. That makes for a 4 volt drop across the regulator. If you have not looked yet, that regulator is small, and not much heat sink provided.
Either way, you can't draw 2 amps (for very long, seconds), from a small 9 volt battery, or through a small 5 volt regulator. I don't know which went first, but it would be a close race.