He said his 12" runs fine so I am guessing it would be in the sub itself. You said some one punched a hole in the sub as well. If it was hit hard enough it could have damaged the voice coil as well. At low volume there would not be enough travel to cause problems. But once the sub starting moving more, it could.
Also, make sure that the tinsel leads from the terminals to the inside of the speaker arent loose or touching the metal basket anywhere. That is another common cause of problems and different volumes.
Lastly, someone here said your amp is 2ohm stable per channel which does not in any way mean that it is stable at 2ohms in a briged mode. 2ohms per channel at stereo is common in almost all amps, but an amp that can handle a 1hom load briged is not as common.
If the sub is 8ohm, that would not be a problem, it would just not play at the full potential of the amp.
If you want to verify the ohm load, get out a multimeter. Select the ohm setting that is closest to 10 or just the ohm setting if is reads all at one setting. Unhook the speaker from the amp and test between the positive and negative. Make sure the cone is at rest and not pressed in or sitting on anything. Cone movement will make the reading change. You will not get an exact 2,4, or 8 but it will be real close to one of them. Let's go from there and see what you find.