From what you described maybe the issue is only a corrupted SD card and/or USB device, because the other options alongside exit in Wii explorer are restart and remount.
Retire any USB/SD from your Wii and try again to enter the homebrew channel.
If it's ok then you must format and restore all the files and folders of your sd or USB.
If doesn't the case then only reinstall the homebrew channel again with your preferred exploit (letterbomb for example) inserting the neccesary files in an SD just like the first time but without formating the console.