I've started experiencing this problem when I reached Sanctuary and had to meet Scooter as part of the main story. As soon as the door to his garage would open my game would stop responding and I was forced to close it. Same would happen as soon as I approached Dr.Zed or Marcus since they also have such introductory cutscenes.

I've tried a lot of things, from lowering my settings to reinstalling the game, but what helped me is shutting down MSI Afterburner, its RTTS overlay buddy-app and HWiNFO that was feeding them info. If you don't have those programs installed - check if you have some other programs that might hook into the process of the game running in the background and close them. Hell, you might even try disabling everything other than the game and Steam itself, worth a shot if nothing else works.

So yeah, if you're like me - try this, I don't guarantee that it will help in your case, but it might since it did help me.