Probably the easiest and cheapest method is to use USB loading. Off course, you will need to softmod your wii and need a USB HDD to load the games. To get the games on the HDD, you have three different options. The first option in to use the wii of a friend (which also need to be softmodded) to rip the games to usb. The second option would be to download them somewhere, but depending on the laws in your country/state it might be considered illegal, even if you do own the games and they can be hard to find.
The third option would be to dump them using a PC, but there are only some drives that are capable of this and I don't think they are still being produced. Off course, you could also simply let someone fix the drive.