Not sure what rationale was used when doing a system restore however, you will need to know what wad caused the brick (if itís a banner brick) and uninstall it. If you donít know then you can use the official N recovery disc to uninstall any 3rd party wads. If you want your game saves, you can extract them from your NAND backup and reinstall them manually since they will be erased if you use the recovery disc.
Nintendo's Offical Wii BackUp Disk v1.31.rar
Edit: You might also look into using the NAND formatter linked in my signature.