I'm not sure about this, but could the issue perhaps be that Friend Code is stored in save? I dunno if it is or not, but if it is, that may be the issue. AFAIK, there's some sort of algorithm that uses a bunch of keys from your wii to calculate a game's friend code, including your wii's friend code (for message board) and some other things exclusive to your wii. it probably checks these and realizes you can't have the friend code in the save you downloaded.
If you can work out were in the save the friend code is (my advice is check the friend code on the wii in the game if you can, then if possible dump your Wii's keys and use FE100 to decrypt the gamesave, and search in content.bin in a hex editor for the friend code from the save.), then you could make a new save on your Wii, let it generate a friend code, and then do the same to it and copy the new friend code to the old save.
This is all assuming that the friend code IS the issue, and that it is stored in the savegame. Before trying all this, my advice is this: delete the save, and see if you can go online by generating your own friend code.
EDIT: OK, I have been looking around for info pretty much since I posted this and have finally found some useful info. Your friend code and friend list are stored in the NET0.bin and NET1.bin files in the save. If you decrypt the downloaded save and a save made by yourself on your Wii, and then put the NET0.bin and NET1.bin in the downloaded save, then re-encrypt it, it should all work nicely. The only problem is I think you'll need the keys from the original Wii the save was made by to be able to decrypt it.
EDIT: Little more reading, and I think you can do it without the keys. Just install the downloaded save on your Wii, use Savegame Manager to dump it, delete the save from wii, copy dump to computer, make new save, generate friend code, dump new save with Savegame Manager, copy NET0 and NET1 from second save's dump to the downloaded save's dump, copy downloaded save's dump to SD card, install with Savegame Manager. Then all should be good. However, seeing as you have a virgin Wii, you may need to (temporarily at least) install a patched IOS. If that's an issue, I don't think you can get this working.