Or use WAM, or WiiMod.use an older, non wii motion plus controller to hack it with.
Or use WAM, or WiiMod.
More simply that search an older wiimote.
IMHO.
Mh.. wait.
But reading better your post, I see that wiimote doesn't work also in system menu.
Change wiimote can't resolve that, but you can try, because seem a problem with the bluetooth module in Wii (but if the problem is really that, is quite strange that the wii boot).
When did you have these problems, you have brutally unplugged the power or you have turned off the Wii by pressing the "power" button for a few seconds?