Stokey, Lucas (1989) p 11 FOC
Your FOC is correct. They took the FOC a step further and concluded that $\lambda_t=0$ for $t&lt;T$. I quote from page 11:


  To obtain these conditions note that since $f(0)=0$ and $U'(0)=\infty$, it is clear that the inequality constraints in (4) do not bind and it is clear that $k_{T+1}=0$


The intuition is that the inequality constraints will only bind when you consume all capital today ($k_{t+1}=0$) or you invest all your capital and consume nothing today ($k_{t+1}=f(k_t))$. Both of these cases (save the former when $t=T$) imply that you will be consuming nothing for at least one period. Combining this with the MU being infinite at zero, obviously this cannot be optimal.