Uninstall the game first from Impulse then navigate to these directories and delete the folder called Demigod:
C:\Users\Your Username\Documents\My Games\Gas Powered Games
C:\Users\Your Username\AppData\Local\Gas Powered Games
After you have fully removed Demigod from your computer login here and download Demigod: https://store.stardock.com/login.aspx?ReturnUrl=/myaccount/products
Once you have installed and registered the game, join an online game and the two new demigods should become unlocked.