You may need to manually remove the game folder, and run the fix below before you'll be able to re-install.
Go to C:\Program Files\Stardock Games\Sins of a Solar Empire (or where ever you installed the game) and delete the main Sins folder.
Once you do this, download the file below (follow the link in IE, as other browsers will simply display it as a text file):
http://sd.stardock.com/curthendzell/sins_entrenchment_fix.reg
Save the file to your Desktop and run it from your machine. Then, reboot your PC and go back to Impulse and try installing the base game. Make sure it installs to 1.15 version, test it out before then installing entrenchment.
If that doesn't help, anyone with this issue should send us an e-mail to support@stardock.com and include your dxdiag info;
Click Start-> Run, and type dxdiag in the Run box, save the information and attach it to your support e-mail.