Generally, you can't do that. The only thing I'm aware of (requires NAND reprogramming) is this.
my wii completely broke a few days ago (beyond repair) but i have a nand and keys backup for it. is there any way for me to buy a new wii and restore my old nand onto the nand of the new wii using the boot mii nand restore, is this even possible? could it brick my wii or should i just leave it. Also does the nand contain saved game data because thats the only reasaon that i want to restore the nand.
Yes, it can be done with Betwiin (the guide you were linked to) and the NAND can be installed on a different Wii using Bootmii. To do this successfully you would have to encrypt the NAND with the new Wii's keys using Betwiin, insert the boot blocks from the new Wii into the old NAND, and attach the keys from the new Wii to the old NAND. I've done this many times but wouldn't recommend anyone attempts this unless they know what they're doing.
The way the OP phrased things, I suspect a mechanical issue rather than a bricked issue (I could be wrong).
If his Wii is like this, then his quest is possible (lol):
LMAO Yeah if it was damaged beyond repair while using it as a jack stand then he's good to go.
The other option you can try would be to extract the game saves with showmiiwads and try installing them on the new Wii with savegame manager. I haven't tried this but it should work (I'm not sure if savegame manager decrypts the gamesaves when it extracts them or not).
This poster had sent his wii to me, but it seems to have gone missing in the post. I assume he's after a new wii and then copy his existing data to it while we wait for insurance claim or it actually is found.