First of all, go to the My Document folder, click My Games, click DK Online (Or just paste C:\Users\xxxxx\Documents\My Games\DKonline (Change the xxxxx to your computer user account's name.)), in that folder you will see a file called "DK.ini" Open this file and change the following to.
WIDTH = 1024
Height = 768
After this you should be able to play.
With love and best regards,