I know this is really late, but I ran into this EXACT same problem. When I initiated the mission I had a romance scene with both Ashley and Liara, then the screen goes black. If I moved around I could hear movement in the game but couldn't see anything. I fixed this in my game by loading a prior save, then performing a quick save just before starting the mission again. I then closed the game and edited my save file with "Gibbed's Mass Effect 3 Save Editor"
http://www.moddb.com/games/mass-effect-3/downloads/mass-effect-3-save-editor1 Under Plot-->Mass Effect 3-->Romance I unchecked Ashley and Liara (everyone but Tali) saved over my quicksave then loaded the game.
After re initiating the mission I had a romance scene with Tali then progressed to the war room (Where I was previously getting the black screen).
This may require some testing. I chose Tali since I started the romance sequence with her by choosing her over the Geth and getting the gift photo of her for the Captains Quarters.
I just figured I'd update this thread with a solution found in 2018 as I'm sure others will continue playing this.
