Did you repaired with Origin or Steam?
If only Steam also try to to repair over Origin.
If that doesn't help create a DxDiag in text file format and post it with your next reply. You can do that with the "Choose file" button at the bottom right corner of the reply window.
@holger1405 Stumbled across this thread when I encountered a very similar issue to this person. I had some really weird stuff happen throughout the DLC. The issue I'm facing is at the end of the shadow broker DLC when you defeat the boss and try to leave. Instead of loading the introduction cutscene with glyph, it instead loads to a mostly black screen, though you can see shepard t-posing. Can't move or do anything except open my menu and even make a save. Though that save does nothing really as it loads you right back into that bugged state.
I'm currently repairing my game files though it will take a while. Just in case that doesn't fix the issue, I preemptively created a DxDiag text file before starting the process. Hopefully repairing the game will help and I will soon find out and if anything can be gleamed from the text file, hopefully, it could also have an answer as to why this problem is occurring.
EDIT: repairing did not work
@holger1405 I have the game on Steam. I ran repair through origin which brought up the steam repair tool. I used texture mods and DLC packaged mods. When repairing it removed the textures and any mods which made any direct edits to the game. I went back to a save before the fight with the SB and it still lead to the same result. The last time I played through ME2 I had mods on then as well though it didn't cause this issue. Having said that though, I know that it can still cause issues even if I hadn't experienced them before. I went to an older save before I started the SB DLC and completed everything else and just used a save editor to add the flags to show that I had "completed" it for my ME3 import. I acknowledge that it was most likely one of those DLC packaged mods that caused the issue.
