You need to install an additional GameCube loder or select a different GameCube Mode to launch GameCube games from USB or SD card.

[BigDaddyWeaves]

See? @CoolMe and @SaulFabre

EDIT: I'm dumping to a 32B HC microSD card -> SD card adapter HC of course. Could that be the cause?
Maybe try dumping it to my USB hard drive? Instead of an SD card?

EDIT: Here's what I get when I try to mount the USB drive for use to rip the game:

 

[CoolMe]

EDIT: I'm dumping to a 32B HC microSD card -> SD card adapter HC of course. Could that be the cause?

Not necessarily. Unless you have sd card issues, or with other homebrew apps then maybe..

Maybe try dumping it to my USB hard drive? Instead of an SD card?

Yes, i would recommend doing that since the read/write speed on the sd card reader is slow anyway (in comparison to the usb port), and less wear & tear to it imo..

EDIT: Here's what I get when I try to mount the USB drive for use to rip the game:

The error on the first pic, it says "read error", and not internet error or anything. means it's either it can't access the data that's on the disc because the disc drive is faulty in some way, or the disc drive is fine and can't read from the disc because the disc itself is damaged or corrupted in some way..
Now, i would suggest trying with another disc to try to see who's the culprit, and try to dump a Wii disc too just for testing. It could be just the laser part (assembly) that reads the GC discs that's faulty, but the one that reads Wii disc is functional..

 

[BigDaddyWeaves]

Not necessarily. Unless you have sd card issues, or with other homebrew apps then maybe..

Yes, i would recommend doing that since the read/write speed on the sd card reader is slow anyway (in comparison to the usb port), and less wear & tear to it imo..

The error on the first pic, it says "read error", and not internet error or anything. means it's either it can't access the data that's on the disc because the disc drive is faulty in some way, or the disc drive is fine and can't read from the disc because the disc itself is damaged or corrupted in some way..
Now, i would suggest trying with another disc to try to see who's the culprit, and try to dump a Wii disc too just for testing. It could be just the laser part (assembly) that reads the GC discs that's faulty, but the one that reads Wii disc is functional..

I'll give both of my Wii's the CleanRip disc ripping treatment. Get back to you two tomorrow or sooner depending on if I have the time tonight. I did successfully rip all my Wii games with my 4.1U Wii. A total of 12 games including some very big ones including Metroid Prime Trilogy. I'll try giving some GameCube games a proper rip with multiple games. Then I'll try the same games with the 4.3U Wii. Sound good @CoolMe?
EDIT: Tried a different USB Port for my game to save to and badabing Paper Mario TTYD is now ripped. Funny how little tricks like that can make such a distinctive difference. Isn't it weird @CoolMe ? I'm glad it's not my drive and that I don't need the internet to rip GameCube games I'm noting that I have to have the USB HDD In the back most right USB port and everything else was cake with the prompts that CleanRip provided. I now feel much more confident in future rips! Which I have quite a few of them. Thank you @CoolMe & @SaulFabre for all the help and not giving up on me. I'll let you guys know if I have any further issues but that was one game I was really hoping I could rip (favorite game) and yes I've beaten it over 30 times, lol. I'm a big fan of the series. First two games were the best. Nice that I can now play them both on the same machine. Thanks again everyone who contributed something to say.

 

[UltraDolphinRevolution]

@UltraDolphinRevolution but I have already backed up my files I just don't think I'll be able to run my PAL save for Paper Mario The Thousand Year Door from my 4.1U Wii that apparently was set up to run all regions on this new set up. Looks like I'll have to start a whole new adventure ohhhh nooo hahaha yeah right like I actually care I beat that game 30-something times already one more time won't make much of a difference to me.

Any Wii can run any regional game with Nintendont. If the save file is PAL, you need to get the PAL game.
30 times? I beat it one year ago after one and a half decade. I had been stuck in the hub village.

 

[BigDaddyWeaves]

Any Wii can run any regional game with Nintendont. If the save file is PAL, you need to get the PAL game.
30 times? I beat it one year ago after one and a half decade. I had been stuck in the hub village.

30+ times @UltraDolphinRevolution !! I'm a super fan!! The game has everything me and my buddy dissected that game and had our power level at 99 I was up to level 49 on my PAL save. I would do the pit of 100 trials once every week for fun.

 

[BigDaddyWeaves]

I'll give both of my Wii's the CleanRip disc ripping treatment. Get back to you two tomorrow or sooner depending on if I have the time tonight. I did successfully rip all my Wii games with my 4.1U Wii. A total of 12 games including some very big ones including Metroid Prime Trilogy. I'll try giving some GameCube games a proper rip with multiple games. Then I'll try the same games with the 4.3U Wii. Sound good @CoolMe?
EDIT: Tried a different USB Port for my game to save to and badabing Paper Mario TTYD is now ripped. Funny how little tricks like that can make such a distinctive difference. Isn't it weird @CoolMe ? I'm glad it's not my drive and that I don't need the internet to rip GameCube games I'm noting that I have to have the USB HDD In the back most right USB port and everything else was cake with the prompts that CleanRip provided. I now feel much more confident in future rips! Which I have quite a few of them. Thank you @CoolMe & @SaulFabre for all the help and not giving up on me. I'll let you guys know if I have any further issues but that was one game I was really hoping I could rip (favorite game) and yes I've beaten it over 30 times, lol. I'm a big fan of the series. First two games were the best. Nice that I can now play them both on the same machine. Thanks again everyone who contributed something to say.

You got the message/EDIT that the problem was fixed everyone? @SaulFabre and @CoolMe ? I'd like to say thank you one more time I'm so very happy that I don't need the internet...after all this time I can finally rip my games with hopefully not too much trouble lol. But if I run into any snags you know where I'm coming! Thanks again! Persistent people like you guys and tinkerer's like me (who tried the whole USB port swap thing) are the real troubleshooters of the world. Enjoy your days helping as many people as you can!

 

[CoolMe]

Tried a different USB Port

You had your external hdd plugged into port 1 instead of port 0 (the lower one when the Wii is in a horizontal position)? When you said you had the partitions and usb drive set up properly, i just assumed that you had it plugged into port 0.. Oh well, glad it works now for you!

 

[BigDaddyWeaves]

I had it plugged in the wrong spot that's why it was throwing that 000000 error when I tried to rip to USB so I thought to myself hrm that could be the problem! Switched them and badaboom it just worked, rather quickly I might add. My notes on the Wii are now heavily cautioned to plug the HDD into the right spot or it just won't work. Since my SD card seems to stall out around 80% the HDD went the full 100 and I was so happy . Thanks @CoolMe together @SaulFabre, me and you have done it!