I'm in the very first chamber after receiving word that the drauger have been awakened by the initial excavation. I've completed the task of clearing out all the drauger, but I can't find a way to delve deeper into the borrow. Is there a chain or button I am missing in that first large chamber where you battle all the drauger?

You have to clear it out about 3/4 times more. Just go back the way you came in, and talk to the guy. He will ask for more monies. Wait 3 in-game days, go back to talk to him, He will say wait, but go back to Raven Rock and a messenger will show up. Do this until he askes for 5000g, and the 3 day thing, and then you can go through the whole dungeon.

Does the "find a way deeper into the borrow" quest objective in the log just stay unresolved for a couple of days in game? I went back to Ralis and he said something about it being good clearing the drauger but there's not much more we can do until we find a way deeper into the borrow. I also did not get an option to fund the next stage of the excavation.

Nevermind, just found a video on youtube that shows how to proceed.

nvm