"I am your father!"
Translation:Ich bin dein Vater!
No, because deinen would be accusative case, which would not be appropriate here.
The verb "to be" links a subject to a predicate that says something about that subject, and such predicates are (almost always) in the nominative case in German.
Hence ich bin dein Vater.
If it helps, you can think of that sentence as meaning "I = your father", and since the two things are equal and refer to the same thing, they are in the same case -- nominative.
"to be" is not an action verb; dein Vater is not the target of the action -- he isn't "being been by me".