Wow! Chinese "quality control" scores again! That said, and with a little help from Google and Google Translate, I found that Foshan Hanyi Electronic Technology Co., Ltd. has several web pages that you can find by using this Google search string: "
who is www.hanny.com.cn" and clicking on "Translate This Page" when the Chinese results appear.
Here is one of the links I got using this method.
Hanyi is a rather large mainland China switching power supply manufacturer, selling in humongous quantities (millions of units) exclusively to the embedded OEM market. You
should be able to find and replace the defective power supply board with one of similar capability (whatever that is), but there is no guarantee that the maker of the humidifier, Tao Tronics, actually specified an adequate power supply, or provided it with any protection against power-line surges or other happenstances that are known killers of these things. There are lots of unhappy customers posting on the web about Tao Tronics ultrasonic humidifiers.
If products identical with, or similar to, your humidifier are available at Wally-World, as you suggested in your post #13, I would go ahead and buy at least two: one to replace your defective product and the second one to reverse engineer for spare parts. Good luck with that.
BTW, those are excellent photos you have provided, and you received some really insightful comments from the EP responders. Please visit here often! Perhaps you would like to try constructing your own ultrasonic humidifier? We can help with that.