Before You Start
The same symptoms do not always point to the same root cause, and physical damage can be tricky to spot. If you are going to attempt your own repairs, it would behoove you to have a spare set of HomePod parts to diagnose and troubleshoot against.
For HomePods that have never been opened or taken apart, start with the common issues of no power, death farts, and boot loops, then work through the less-common ones. If you diagnosed a known issue, made repair attempts, and now have a new problem, it's probably your fault: check common mistakes.
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This is a collection of what I've learned, found, and fixed over the years and thousands of HomePod repairs. Check back often, as I'm always adding new issues and fixes. If you think you've found a new issue or fix, let me know and I'll put it here with your name on it. Rather not do it yourself? Mail it in.