I installed Japanese input language for the sake of screenshots, let's see if we can fix this for you.
First things first, the basics in using Japanese input language. If input language is installed and enabled, you will see it on your input method selection dialog:
When selected, the Japanese input language shows two icons (my Taskbar is vertical at left, image might look different than the same on your display):
1 = Japanese input language active
2 = Keyboard layout selector (by default Half-Width Alphanumeric)
You have to right click the keyboard layout selector (2) to select either Hiragana, Katakana or Alphanumeric layout to type using the layout you need:
You can also select one of two input methods, Romaji or Kana:
A bit confusing although somewhat logical default behavior of Japanese input language might cause user to think the Japanese is not working, as it defaults to Half-width Alphanumeric keyboard layout which is basically as an English layout, using western alphabet.