Think about it!
If the user is to write the whole date in manually, it will most certainly open for a whole lot of "error-typing" and mis-spelling.
I am convinced that the best solution is to force the user to type the date in the correct format... Or, at least, dividing the input for the user.
Remember, you don`t HAVE to use dropdown.
But you should divide the input into separat input-boxes.
[YYYY]-[MM]-[DD] [hh]:[mm]:[ss]
Then you can reconstruct the input boxes to suit the most common way of inputting dates.
Because that is different from country to country:
[YYYY]-[DD]-[MM]
or
[MM]-[DD]-[YYYY]
Another thingy:
If you go for one input box, then you`ll propably have to write lotsa code to reconstuct the date into the correct format...