It sounds to me like it may be the fault of either the wii mod chip you had installed (which one did you install or have installed?) or the modification job itself, which can create a problem like this.
The discs should always read, no matter what. In all the wii's I've modded I have never had this type of an issue at all.
Do you have the wiikey setup disc? You can use this to setup the wiikey (as it may have lost the settings!) This disc will only work with the Wiikey though,. and not any other mod chip.