You're supposed to try and activate the doors. You go downstairs at the start, try and open the locked door. Then you go back upstairs and try to activate the door, even though it's locked, then a voice in your head will tell you to kill the other man. If you just wait a bit he will attack you, then you go downstairs, through the door, and continue downstairs until you get to the shrine. There's a hole in the wall in the basemant you follow down.
Normally yes that's how it would go, but the only reason you go downstairs in the first place (aside from your own decision-making) is because the man you came in with is supposed to have heard a noise and run down there and you follow him.
The problem is the player walks in the house and the man says a bit of dialogue and then just stands there. If he doesn't move or doesn't run downstairs then at that point you know the quest is glitched and reloading a previous save is so far the only way to fix it.
It happened to me as well. Luckily I had a save to revert to and when I tried it again it worked.
For Bethesda's reference, this is what happened to me:
I follow the man inside the house. He walks to the center of the room and crosses his arms, saying his first bit of dialogue. At that point nothing else happens. I go and explore the house. Everything works as normal. I go downstairs and attempt to open the basemant door which triggers the house to begin shaking for the first time, complete with the possessed pots and pans and junk flying around madly. Eventually this ceases and I continue looking around for a key. Eventually I give up and attempt to leave. The front door is now locked and I cannot get out. The house begins to shake again and junk begins to fly around however this time, it does not stop. Eventually I save the game and decide to kill the man I came in with since I assume (since he's just been standing there the whole time) that he's in on whatever is going on. I kill him and I hear Molag Bal talk to me as he would've had he commanded me to make the kill (such as he should have had the glitch not occurred). The basemant door is now unlocked and I proceed down to the shrine. From here on out the sequence plays out as normal. Molag entraps me and explains to me what has been going on and what I need to do.
I go back upstairs but the door is still locked and I am trapped forever. lol
I revert to the save the game made for me when I initially entered Marcarth and I follow the man inside the house once again. This time, the quest plays out correctly and he runs downstairs to investigate, instructing me to try the basemant door and so on. As far as I can tell, there were no other changes made by me in order to fix the glitch aside from reloading a save so I'm guessing it's a technical bug I can't influence.
Hope this helps