If only it was that easy. There are unique keys in the Wii that somehow make it impossible to just transfer another Wii's NAND.
If your BootMii is installed as boot2 (not IOS) and your SD card has the proper files for BootMii to run... and you still get a black screen, then your boot2 is probably corrupted. If so, then...
Sorry to say, but I think your Wii is bricked for good... unless you can extract your keys physically using some equipment, which is "possible". Then those keys would have to be patched into another NAND backup, which... well... just check this link out:
http://bootmii.org/nandflashfor all the trouble to go thru... unless I knew someone who has the skills & equipment, I personally might be tempted to just sell the brick to someone willing & able to meet bushing's requirements. Of course I might also be tempted to buy the equipment if it's not too expensive and make it my next little learning project... but that's just me. I would definitely need A LOT of help, since last I checked my soldering skills are total fail.