This is mostly just a post for my personal reference:
After mucking around with the phone, plugging in and unplugging things from its USB port, the port may suddenly stop working and the phone won't even initiate charging when the charger is plugged in. Soft reboots or soft power-down/power-up doesn't appear to fix it and the phone won't appear when plugged into a computer's USB port.
The solution is somewhat simple: Force a hard reboot by holding down the power button for 10 seconds. The following reboot, it appears to work again.