This is not making logical sense. If the second speaker plays, then it would mean you have a short in the first. If you have a short in the first, then touching the battery should not have produced 'sound/movement.' You did isolate the first speaker when you touched it to the battery, so it was not the second making the noise and movement? I am sure you did. Next step is a VOM. Why? Very unlikely, but it is possible that you have a short across a section of the coil so that it is using only a couple of turns. A nine volt battery will make it move, even if only a couple of turns were left. Resistence would be very low and probably less than an ohm. The speaker should still work by itself, but at much greater diminished performance than the others.
If you isolated the speaker and ran an audio signal through it and it would not play, I would toss it or recone it, depending on the expense of reconing. I am hardly an expert in electronics, but this is not rocket science, and the piece seems undependable. Reconing maybe $50 or less, depending on the speakers and kits the shop is using. eBay sells about everything, and you can probably find a suitable replacement for around $25, but time is money, eh? SWR should be your best resource in this case, if it has to do with the attenuater. Without being there to inspect it, this is all I can think of. I wish I could do better here.