OK the most likely scenario here is that the owner of that Wii used an app called DOP-IOS MOD. Certain versions of this app (v 11.3, 11.4) have a bug which cause the issues you describe. They then likely upgraded to system menu 4.3 thinking it would fix the problem. Upgrading to 4.3 makes the situation worse because you no longer have working exploits like Bannerbomb and games don't work so you can't use game exploits. If they didn't upgrade to 4.3, the fix would be to simply run a Dop-Mii system check. Unfortunately you only have a few options at this point which I'll list in order from the easiest method to the most difficult.
Bootmii Method - If the console has Bootmii installed as boot2 you can use that load Dop-Mii and then run a system check. You could also just reinstall the working backup if you like.
System Menu v912 Downgrade Disc - If the owner had mauifrog's softmod with a patched IOS80 this method is possible. You can do a Google search for instructions on how to use the disc to recover from this bug along with the requirements.
Flash NAND With Programmer - This is the most difficult way but the Wii is 100% repairable via this method since you have a working backup. You can read my guide here http://www.wiihacks.com/bricked-wii-...ing-guide.html
FYI - Updating the system menu doesn't return the Wii back to stock. This isn't a stock Wii.
I'm moving this thread into the bricked section where it belongs.