Have been waiting many game hours after giving the lexicon to Septimus but have had no contact, visiting him gives no new dialogue options for the quest (discerning the transmundane), can anyone help me out?

This is a Daedric quest. Check your quest log to see if you have activated the next part of the quest.
After talking to Septimus and giving him the completed Lexicon was Hermaeus Mora's avatar blocking the exit to the cave?

Side note: You must be level 15 to start the second part of the quest, which is the completion side. The reason he gives you the object in the main questline is because you require it to get into Blackreach.

Nothing was blocking my exit, and my quest log still states "He will contact me when he has the secret"

How were you contacted?

Courier, he gives you a letter at some point, I have no idea how long it took, I was afraid the quest was bugged, but he turned up alright

Bumping existing thread.

I can't get the lexicon to transcribe.. or whatever.

Took the elder scroll... but the quest didn't update because I didn't grab the lexicon. I can't pull it out of the machine without fiddling with the machine and then it says its blank again. If the lexicon is glowing blue in the machine I cannot remove it.

WTF.

I have the same problem

I just finished this quest (both parts) and I have some concerns:

First, the Oghram Infinium: Is it supposed to just disappear after reading it? I used it and leveled up (twice!) and it was still in my inventory until I closed my inventory. When I went to put it on a bookshelf at home, it was gone.

Second: The Essence Extractor doesn't seem to have an in-world model. If I drop it from my inventory, it just disappears. Nothing is dropped, but the item is gone from my inventory.

Thrid: The Elder Scroll, Lexicon and Attenuator are in my inventory (the extractor and lexicon had to be looted off Septimus' body) but I can't drop them as they are quest items. The Elder Scroll may serve another purpose, but FFS it's 20 pounds. FOR A PIECE OF PAPER?! The other two items though... I don't see why they are still un-droppable quest items. I mean, the Lexicon alone shouldn't be since there really is no reason to loot Septimus at the end unless you wanted those two unique items to display in your house (like I did).

For those who can't solve the puzzle: I just kept hitting buttons until the other buttons became usable and then I kept hitting those until the thing opened.

Lol. Theres a glitch concerning this book, I used it and now I'm level 67. If you can load a save before you used it, you should do the glitch. The glitch is long to explain, but google it.

Too long? It seems you just put the book on a bookshelf after you read it for the benefits, as it won't delete the book when it's on the shelf, so you can take it again and you can keep reading it.

I had the same problem I think. You have to fiddle with the buttons on the pillar until they all work and then the lexicon separates so there's two halves hovering around a glowing core (I might be getting this sequence wrong). I just worked the buttons in various sequences from right to left, there is probably a logic to it but for me it was just trial and a lot of errors.

My problem is I got the lexicon back to Septimus, got the blood, the door opened and we went inside. He remarked on the book and the quest marker hovers over his head telling me to speak to him but he's perpetually busy. I left, returned a couple of times to no avail, he's still busy. I just checked my journal and it's reverted to "bring the blood to Septimus", the door is now locked with him inside!

Ok, so I think I was contacted by the courier, he came up to me, did his little "for your hands only" thing and I got a message saying "item(s) added," then nothing. I have no letter from Septimus, no Essence Exctractor, nothing. Anyone else have this issue? Or am I alone in this?

Sell it to the orc librarian at the College in Winterhold.

Solved my problem by using the console, which I hate doing, to reset quest to the correct stage, then to set collision to off. I went through the door and I read the book, Chose Shadows.

Quest stages http://www.uesp.net/wiki/Skyrim:Discerning_the_Transmundane.