So, Neloth sent me to get this staff in High Gate Ruins. But the last room where the staff is the doors are shut and I can't find any way of opening them. Anyone know how to get in there??

Did you meet with Anska when you entered the ruin? The door may be locked unless you first talk with Anska.

i'm trying to remember exactly which quest this one is... you had to go back to skyrim to get it, right? well if it's the one i'm thinking of and is in a cave.... did you harvest glowing mushrooms off the wall and place them in that fire pit? i don't remember any doors past that point, you just go through a lot of caverns and end up at the treasure chest.

(if that's not the correct quest cause i'm at work and can't check.. then just nevermind! hehehe)

this same bug happend to me but with the quest from Neloth:wind & sand.

the only way I was able to get around it was to use the wooden bowl shout thru the walls and try to land on solid ground IN that chamber. It did work after a couple of hours ~ at first it was frustrating but after the first hour it became a fun. Because of the challenge of getting my timing down precisely to land on solid ground and not fall thru the world and end up at the entrance of the zone LOL.

they should add some tough quests like that where perfect timing to land on solid ground must be precise and not fall into the abyss. Fall into the abyss could be absolute terror for your char and lead to another quest both with different rewards LOL.

You are thinking about Lost Echo Cave.

This is from the UESP wiki, bugs section:

If the Radiant quest http://www.uesp.net/wiki/Skyrim:Fetch_me_that_Book%21 or http://www.uesp.net/wiki/Skyrim:Shalidor%27s_Insights has been accepted and directs the player to High Gate Ruins, the book will be located in a chest in the antechamber behind the Throne Room. However, the antechamber will be inaccessible if the player has already visited High Gate Ruins and killed Vokun.

• This can be resolved by using http://www.uesp.net/wiki/Skyrim:Console commands, either to resurrect Vokun and kill him again (select the body, not his ashes) or to simply pass through one of the closed gates (use 'tcl' to turn clipping on and off).

I already did the quest with Anska a long time ago, way before dragonborn came out. And I can't use console commands cause I'm playing on the 360. I guess I'll try the plate glitch. I'm not sure how it works though. I've watched a youtube clip of it but never tried it myself. Don't see any other way though.

Same thing happened to me on the Alteration Ritual spell.

You see the arrow, for the thing you get, in the last room of highgate ruins. The priest is dead, the gate doors won't open.

I just tried the plate glitch myself, for about an hour plus today. I could not get it to work at all on the gate, but did get it to work
on the wall sort of (like twice...) Both times I got it to work on the wall, I managed to hop through into a blue area but evidently
it was too far to solid ground, since I just zoned back in at the start of the priest's room (luckily without having to "load" again.)

I tried it with two different large platters, two smaller plates and a couple of bowls. I later found a couple of the wooden plates,
but have not tried them yet.

I too watched the video(s) on doing it, so I think I have the jest of it. Hmm.. I never tried using it on the OPPOSITE wall, away from the
arrow for the item (mine is an arrow behind the LEFT gate.) My guess is the right gate leads over to where the left is?

It still amazes me that Bethesda never saw these as things they had to fix. Several quests can lead there evidently, INCLUDING
ONES IN THE DRAGONBORN DLC? Do these guys even KNOW what bugs they have? Then they make it for the xbox 360 FIRST?
I'm surprised Microsoft still licenses them.

By the way, my guess is saving just before he gives you the quest would not help. I remember doing this, at the college, before
the Alteration Ritual Spell sent me to Highgate Ruins. When I saw the bug, then read about it, I reloaded that save. EVERY
SINGLE TIME, when I get the quest, the guy still sends me to Highgate Ruins. There are around four places he could send me,
but its like the game knows I will be sent there even before I get the quest from the guy.

I believe the location of Kohvazein's fang is set at the begining of the game, like Meridia's Beacon. I am pretty sure I picked it up once before getting the Alteration Ritual quest.

it is i have done that that mutiple times

From uesp

Vokun's Throne Room may be accessed by utilizing a follower to open the gate blocking the player from the antechamber exit above the first room. This is accomplished by bringing a follower after clearing out the entire dungeon (unconfirmed if clearing out the dungeon is necessary), climbing up the pile of rubble, in the first room, beside Anska, and using Whirlwind Sprint to access the walkway leading to the exit from the antechamber. The follower will run through the dungeon and eventually, in approximately 1-3 minutes, appear on the other side of the gate from the player. The follower can then be instructed to pull the chain, thereby opening the gate and permitting the player into Vokun's Throne Room.

Tried this previously, it works fine.