Not sure how helpful this might be (especially if you have repeatedly read this or a version of it before 
), but perhaps the best thing to do is give a call to Nintendo's 1-800-255-3700 (6 am ~ 7 pm Pacific, everyday) Customer Service number, and one of the service representatives can do some over the phone troubleshooting to determine exactly what the problem(s) might be with the Wii LAN adapter and your wireless router(s), and then talk you through any needed steps to correct this.
And then if still no luck, they should be able to offer some other suggestions depending on your exact Internet setup on what you need to purchase to play your video games online.