Hey guys, great news! I've fixed it! I'll write what I did here so other people with the same problem can get help.
Basically, I used giantpune's nandBinCheck to see what was the problem. For me, it was a bad HMAC for "/meta/00000001/00000101/title.met". So, I had to download FSToolBox, find this file, press minus and then press plus, it does something I don't understand and voila, it's fixed. This "title.met" thing was corrupted, occupying over 5Gb of Wii Memory (or less, maybe 500MB? Dunno), so when I did that with FSToolBox, it returned to be only 17KB in size. There was some other minor problem with the Weather Channel, but deleting it and reinstalling with DOP-Mii fixed it.
Anyway, thanks for all your help, I appreciate it!