If none of the mids or tweeters work, then any loose wiring would almost certainly have to be ahead of them, since four separate drivers couldn't possibly all become loosened. So, no, it wouldn't seem to be useful to examine each driver.

Connecting the left speaker to the right channel shouldn't indicate anything, since if the left woofers are working that means that the left channel of the receiver is still operating.

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Enjoy the music, not the equipment.