OH. MY. GOD. THANK YOU!! I have been banging my head on a freaking ROCK for the last few hours on this!
----------------SPOILER ALERT BELOW---------------
So, a couple of points:
1) If you DO NOT see the bomb explosion in the beginning of the Shadow Broker DLC after going with Vasir to the hotel, RESTART your mission. I don't know if picking different squad members helped or not, but if you do not see that explosion, you'll get to the Liara/Vasir shootout and Liara will just be standing there with her pistol drawn and you can't interact with her or anything else. This is where I restarted and realised I didn't see the hotel explosion in the beginning.
2) The "screen going black" car chase - I removed the "-nomoviestartup" option and that fixed it! I did notice that the cutscene seemed to be a different resolution than the one that I was playing at, so maybe a factor?
TODO: Curious if the outfits the team members wear matters; I outfitted them all with the DLC custom packs. If I could do it all over (Which I distinctly DO NOT want to do, maybe I'd try with their default skins.
THANK YOU again for this!