If your power supply blew the ramps board, it likely also blew the arduino voltage regulator. Aside from the polyfuses, nothing on the ramps is particularly sensitive to voltage up to at least 24v, and I think possibly 30 or 35 (but I might be mistaken about over 24v).
If you want to test the arduino mega alone, plug it in to a computer and try to load a blink sketch example. If you can load it, unplug the USB cord and plug in a power supply > 6V but <= 12v into the barrel jack. If it blinks again, the basic operation of the Arduino works. That doesn't guarantee there isn't other damage however with particular pins.