I've found that most microphones stop working because the solder joints on the XLR plug come undone. I'm not sure what type of connection the SM57 has, but that would be the first place I'd look. If it has screw terminal connections, simply loosen and re-tighten. If they're soldered, visually inspect the joints for a dry joint or simple broken connection.
In some other cases, I've seen the pickup element itself become unsoldered, usually due to someone unscrewing the windscreen and accidentally pulling on the element.
If neither of those things are the issue, I'd take the entire thing apart and look for loose or broken connections. When you get down to it, they're really pretty simple devices and almost all the issues I've seen are physical-connection related.
(Also, I'm sure you've checked this, but make sure you're using a known good cable that works with another mic on a known good channel.)
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