Honestly I would switch to USB Loading at this point. I do have a few suggestions you can try looking into. But I have not used discs in years so who knows if they are any good...
Notwithstanding, a few things could be happening. modchip issue, dvd drive issue, software issue, discs issues.
Discs got scratched? Check the easy things first! Same thing below, check easier things first.
For gamecube games try running the backup discs from nintendont. It is supposed to be able to play gc games from backup disks and doesn't use the mios, so it can tell you if at least the disc drive is working for burnt backups. Plus it's really awesome and allows you to use all sorts of cool controllers with gamecube games.
For wii stuff, you could also look into something like neogamma and how to set it up and see if your backup disks load from that program (may have to install a different mios for this to work)... The problem is that very few of us are still using discs at all. Even the people who had modchips likely moved over to usb loading.
the modchip has came loose, it's chip stopped working
For this replace the modchip or reseat it. I have heard the clip on modchips sometime don't stay seated as well as some that are soldered on.
the dvd drive has become unreliable, while still reading official disks; it may have stopped reading others.
For this replace the dvd drive. Alternatively the pots could need to be tweaked. Look up pot and gamecube drives and pot and wii drives to get an idea of what to try and tweak.
Some software on the wii has gotten messed up...
flash your backup nand to the system and see if it works again. Or if you don't have that try running modmii and tell it you want to start from scratch. Follow the part of the guide where you reinstall all the cios and ios stuff.
Hopefully something above is useful. Good Luck!