The demo only has episode 1, so no unlock.
Just the small price you have to pay for using the free version.
In Higurashi's case, the demo didn't even have the character portraits, so you're actually pretty lucky.
...But because I'm such a nice guy,
here is a version that will give you a fresh state, give you chapter select from the start, and won't go crazy on the title screen when you complete it, I think. Just replace the nscript.dat in your English folder with this one.
And this should only be used on the demo version.