Never push a cone in and out, not to see what kinda excursion it can do, and not to see if it feels 'blown'. You can very easily push a speaker out of alignment and end up rubbing the coil/former. You could be ruining the perfectly good sub you are trying to diagnose. Also, feeling the sub for free cone/coil motion will not give the whole story anyway. You could have a shorted voice coil and the cone would still appear to move perfectly normally, but a quick check with a DMM would show the short in the circuit (would read 0ohms).
You said the subs are dvc wired parallel, are they wired to each other as well, creating one single mono load? That appears to be what you meant. And if so, I do not see how one sub could break a tinsel lead, short out a coil etc without the shorting the entire circuit. If this were to happen, both speakers would stop playing, not just the one. So either you do not have the system wired as you implied (all coils paralleled into a mono load) or the problem is not one of those things.
Good luck and keep us posted.