Is my Arduino possibly broken?
Considering that you used resistors to lower the 11.5V to an cough - cough "very normal and regulated 5V", that most certainly is the problem.

The "right and cheap" way to lower such high voltage and connect them directly to your 5V (just assuming, since you said that you used resistors to protect the Arduino) is actually to use a voltage regulator. Any cheap 7805 should do the job. The Arduino actually has its own voltage regulator on it, if you connect it though the Vin pin.

The "true and efficient" way to step down some voltage is actually to use a step-down converter. The way this is better then any normal regulator is that a regulator will lower your voltage by creating heat when the step-down converter will do it in a more efficient process.

The USB of your PC might also be the problem. There is a fuse on the Arduino and one in almost all USB ports of decent PCs. If the voltage spike is high enough, it might have burned the port. That is quite a rare event, but still possible.

Need anymore help, just comment. I'll be happy to help you!