You might be screwed. In order to restore your wii you need either a) a backup of your wii's nand in a functional state, b) the ability to install wads to reinstall your system menu, or c) the ability to connect online to upgrade/downgrade.
You can't do a) because you made a backup of your wii's nand after it was already bricked. You can't do b) because you can't navigate the wad manager menu's without working wiimotes. You can't do c) because you need to set up a new connection, but cannot because you can't access the system menu.
You could try to get a different router and hook it up at your house. I'm not sure if a new connection will be needed to be set up, but it might work if you just plug it in like your old one. If you can't restore your nand, install wads, or connect online, I don't see how anyone could fix your wii.