You can't just guess with a powered subwoofer. Randomly "trying" things is a sure way to blow the audio system of your pin. If in doubt post a picture, make & model of sub and others will help you out.

In the audio world the striped wire is *usually* the negative. But that being said, as far as audio goes reversing the positive and negative would only put cause the audio to be out of phase, that in itself would not cause damage to the output amplifier. From the amplifier to speaker it doesn't matter at all in a mono system, in a stereo system it doesn't matter as long as each speaker is connected the same way to keep them all in phase.

The common mistake is connecting amplified audio from your device (pinball machine or whatever) to line inputs of a powered subwoofer. Basically, it's connecting the two amplifiers back to back is what causes the damage. If your input signal is amplified already, you would need to connect this to special inputs(usually called 'speaker level' inputs). This special input has impedance matching components to reduce the input level back down to the line level that the subwoofer's amplifier can use.

Your negative wire is on the wrong terminal, it needs to go to the negative terminal closest to the positive (one terminal to the left)

"powers" from the negative? What do you mean - you have audio working then?

Breaking this down....
Try the sub with a home audio system, if it works fine the problem is the game sound system. If it does not the problem is the sub.

Hook up a regular game speaker for the game, does it work now?

My hunch is either you have fried the sub or fried the games audio system, one or the other.

This is correct statement for POWER wiring. The convention for audio wiring is that it does not matter as long as you connect x to x and y to y. Nine times out of ten you'll find that audio folks use the striped wire as negative, and nobody is going to punch out the the tenth guy who decided to designate his striped wire as positive in his audio wiring.

btw..I'm the tenth guy.

Yes, if you are tapping directly off the games speaker terminals, then you would use the lower pairs of terminals marked speaker level input.

Except maybe the windows of your neighbors house