Installing HBC shouldn't cause any issues with disc reading.
Perhaps you installed some patched IOS or something? Those can cause issues. Either that or sadly your Wii's disc drive is malfunctioning, and the timing is rather inconvenient. The lens could be dirty, if you can try using a DVD lens cleaner (I think there are Wii specific ones, but I have heard people advising the use of regular DVD lens cleaners. Never actually seen any results of this though). Also, are the discs you're trying to play dual-layered discs? (Games like Super Smash Bros Brawl and Metroid Prime Trilogy are dual-layered) Some Wii drives can have trouble with those.
Sorry I couldn't be of more help.