Each major Media Center version has its own installation so installing Media Center 26 doesn't replace Media Center 25. If you're using any of the Windows startup options in MC25 (like Media Server or even Media Center) when Windows starts, you might want to go into MC25's settings and disable those. It kinda sounds like MC25 has the file association for the .mjr license file. If that's the case, ignore licensing MC26 for now, instead start Media Center 26 from the shortcut in the start menu and see if MC26 starts then.
Just double check make sure you're starting Media Center 26 (and make sure Media Center 25 isn't running if that's what you desire). Once your MC26 settings and whatnot is where you want them, you can uninstall MC25 if you don't need it anymore (and no, uninstalling MC25 won't affect your MC26 install) and try using the .mjr license file if MC26 isn't registered (of course, you could manually register MC26 by copying and pasting the registration key when it asks).