You could try an Emulator. Its a clever [technical term]do-dad[/technical term] that sort of translates one type of program to another. So! If you got a Gamecube Emulator liiiike 'Dolphin', for example, you could find an ISO of your game or figure out a way for your CD drive to read the little Gamecube disks. I'm not sure if a normal CD drive can read them but worth a look.
There are a couple of problems though...
1) Downloading the Emulator is perfectly legal because its 'Freeware'. Downloading ISO's or ROM's isn't...While copyright theft is incredibly hard, ney! Nearly impossible to track down on the internet you can get away with anything. Just don't have all these ROM's hanging around your hard drive when you send it to PC world or something.
2) The more important problem is how fluent the translator is. So far, boffins with far greater programming powers than mine or anyone I know, have only gotten so far with your dreams of playing old games with new tech. Up to around the N64 level of complexity in the programming and everything appears to be fine. The best PS2 emulator I mentioned works but only just. There are still little bugs in the program for the emulator to be a substitute for the real thing. Dolphin isn't much better, I found. The boffins haven't got their programs up to scratch quite yet.
In conclusion: try it at your own risk. Do what you can to figure out how to speed it up or wait for the thing to work properly.
Also, my PS2 tends to be rather picky. Without modding, it might not like having a Gamecube game being shoved in it. Even in the guise of what it likes.