Should one include grants that were not finished on the CV? If one gets a grant, and by some reason (e.g., administration problems with the university) the project needs to be ended before the grant is over. Should one list such grant in the CV? or just let it go into oblivion?

If put it into the CV is OK, then should one state that the grant ended before its time? or even state the reasons?
The main reason to include a grant on a CV is to show that you can get a grant, which you did. Whether or not you made productive use of the grant is generally measured from the publications arising from the grant. You can provide explanations, if necessary, in accompanying letters -- a CV does not contain explanations, it just lists the essential facts.