Welcome to Android Central! First, uninstall the task killer app. These usually don't help that much, and can be counterproductive.
Next, can you get to your App Manager? Tap the menu button there and Reset All App Preferences. This should clear out the default for the Home button. The next time you press the Home button, it should ask you which launcher you want to use--select Nova. If the same problem occurs, do the same process over, but this time select TouchWiz.
You may want to boot into Recovery Mode and wipe the cache partition, which won't erase any personal data. Wiping the cache partition can sometimes help with various issues like this.
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