Finitely repeated prisoner's dilemma without sub-game perfection
There is also no NE which sustains coopration for more or less the same reason as in the SPNE case.
Consider, a PD played twice. A strategy contains five actions, one for each decision node: one in the beginning (empty history) and one for each of the four period-2 histories (CC,CD,DC,DD). I claim that any strategy other than (D;D;D;D;D) is dominated.
Consider any strategy in which you play C in period 2, say (C,D,C,C,D). A deviation to (C,D,D,D,D) is profitable because defection cannot be punished after period 2 as the game ends. Behavior in period 1 cannot be conditioned on the future. Given that any equilibrium candidate has the structure (_,D,D,D,D) cooperation in period 1 is also dominated.
If you are not convinced, you can write down the game with all its strategies in a big normal form matrix.
You can iterate the argument for any (commonly known) finite number of periods.