This is something a bit different that I did a couple months ago. I'll start off by saying the Wii U Kiosk owner should consider doing this fix to their monitor. It is cheap and easy to do if you have any experience with a soldering iron. The monitor is fairly easy to pull out and dissassemble.

As an overview, there are three boards, a logic board, a power supply, and a backlight board. I theorized that it was just cheap capacitors as I still heard a buzz coming out of the speakers. Because there was a buzz, I figured that the audio amp was fine.

I started out by making a cap kit. Most of the caps were cheap, I ended up replacing all of them except for one of them on the logic board, of which I mistaken it for another value. Most of the caps were mediocre in quality, brands like Chong. 

The replacement went really quickly. Ultimately it ended up bringing the audio back. It turns out the sound quality isn't actually all too good. I might look into replacement audio amps and whatnot to try to reduce the noise. That said, I believe the issue was on the logic board, but it could have been elsewhere since I just shotgunned all the parts. With that in mind, all the power supply and backlight board are actually off-the-shelf PCBs that you can buy on ebay. The only thing that is proprietary is the logic board, which was made by Lynx. 

Attached is the Excel file I used, it is not complete because of the previously mentioned capacitor being the wrong value, I apologize for that. I would take this list as-is, as mine may be different than yours ultimately.

Wii U Kiosk monitor.xlsx