I'm on Steam, and I've played through Ep 1 without issue. However, Ep 2 never works. Generally, it takes me to the loading screen, then it goes to a black screen with the TWD cursor, all the while playing the audio track from the game.
The weird part is, it's actually worked once before. I played up to the part where Lee starts hacking away at that guy's leg, then had to get off. Since then, it hasn't worked.
I actually went and played all the way through Ep 1 again, hoping I could continue that save. It still doesn't work.