First I found a YouTube Video that showed how to fix it. I was able to do it fairly quickly since I had the same issue a year ago. I bought the part for $7.99 from eBay so I assumed I would just do that again.
Wrong! The cheapest I could find on eBay was for $28.99. Ouch! So I looked up my old order and bam! - they don't sell on eBay any more. So I did a web search and found the same part from the same store for $7.99 - it was simply a standalone website vs an eBay seller. Still not confident in some tiny website, I checked Amazon.com. No love - it was $34.95 plus $4.95 for shipping. Well, the site takes paypal, so I ordered it.
Well, it took about two weeks for it to arrive - it had to go all the way from California to Arizona so mostly I thought my order had been lost.
Oddly enough though, by the time the part arrived, my Wii U gamepad started working again.
So now I have an extra part in case it fails again. However, I can tell you that the video works because I did the same thing a year ago. If I do have to replace, I'll see if I can get some pictures - just in case it helps anybody else.