the wii can be fixed with a few different methods.
first see if it will boot up into maintenance mode. i doubt it will, but it is free to try and only takes a minute. if you are able to, then you can delete the offending channel however you want.
the next method would be if you already have a save exploit installed to your console ( Eri Hakawai, any of the lego ones, Yu-Gi-XXX ). you can set your modchip to autoboot and load the appropriate game from the black recovery menu, and trigger the exploit to load whatever program you want to delete the media player channel.
if you dont happen to have a save exploit already existing on your console, you can try the "fill up the nand and then try to install a channel" trick. basically you go to blockbuster and rent some games that are known to create huge save files. then boot them with the same method mentioned above and let them create a save. once you have your nand filled to a certain limit, you can boot mariokart or another game that has the ability to install a channel. and when you try to install that game's channel, it will say you need to clear up some space on your console, and kick you to the portion of the system menu that allows you to delete channels. and from there, you can delete the media player channnel.
the next method is to use smash stack PAL/KOR. it is a bit of a hassle because you first have to get on ebay or whatever and import the game. then you have to do a bit of trickery to get it to actually boot from a usa wii. once you have it booted, you can use the smash stack exploit to load whatever program you want to use to delete your channel.