No matter where you bought your copy of the game from, you can use your license key to unlock the full version of the game from any source. So if you bought the game from Impulse, you can use the license key to unlock the version that is direct from our site, and vice-versa. In Impulse, to find your license key either just look in your original purchase receipt email, or right-click the game in the Impulse client and hit View Registration.
Once you have that key, you can use it to unlock the "demo" from our site and turn it into the full version, or you can just skill all of that and get the update zip file from our News forum and just unpack that on top of your game files from Impulse. Either way should work just fine for you. Also, probably uninstalling the game and reinstalling it on Impulse would work, but that's kind of tedious (I'm sure the Stardock staff would have better things for you to try with their client when updates fail).