Same problem here, reïnstalling (with reg-fix and delete all the content under c:\Program Files\Stardock Games) does not fix the problem. I can play SOASE without the entrenchment update, but when I install Entrenchement the screen is going black for a few seconds, then I return to the desktop where in the taskbar SOASE is visible but can't activate. I've recently updated my videodrivers (nVidia 8800 GTS512) and other games works fine.
OS : Vista x64 Ultimate
HW: quad core Intel, 4 GB Ram, nVidia 8800GTS512
For now, I deinstall everything and I just install SOASE and hope there will be a fix for Entrenchement soon.
PS. on my laptop (vista 32-bit) Entrenchement is working fine, so maybe it has something to do with x64??