If you need help navigating the halls of either of the public libraries in Ghostbusters: The Video Game, then this walk through can take you from beginning to end.
Outside
Once you wait through all of the cut scenes, approach the moving lion statue. Two ghosts will make tracks into the building, shoot at them, and they will flee again. (Insert a cowardly lion joke here). Give each one a try and then equip your PKE meter. Head down into the lobby and take the door on the right. You are about to enter the Reading Room.
Book Golem 1
Once you get to the front third of the room, your book golem will appear. This one is stronger than the ones you have faced in your previous golem encounters. That being said, your strategy remains the same. Wear him down (your new attacks are handy) and use the capture stream to slam at his focal point. You will encounter a few other golems in this level, and all will be taken down the same way. Once this is done you may have the urge to bail. Before you do so open the door on the far left hand corner and PKE it to get a possessed portrait.
Chasing The Grey Lady
You will follow the Gray Lady through a few different areas of the Library. When most of the time, you might have to listen to the original Ghostbusters whine about how she keeps shushing you. You will be getting near the end of this chase when you reach a room where the bookcases start moving to block their path. Just keep walking the maze, and taking the open option until you reach the other side of the room. Yes, this means that you may end up back tracking every once and a while. No, you cannot use your proton pack to speed things up.
Eventually, you'll find yourself confronted with The Gray Lady once again. In a very frustrating move, she once again leads you deeper into the library. Continue with this game of chase for several more rooms. Don't be too thrown off when she summons both book bats and golems to make your life difficult. Handle this the way you would any other proton pack fodder and keep on chasing. Make your way into the children's reading room and use your PKE meter to find a trophy, there will also be one in the special collections room. Eventually, you will be confronted by two unpleasant ghosts with shields. Capture the shields, and toss them away before you attack them. Otherwise, you won't do any damage. Once the room is clean, put your meter back on and use it to find the secret passage in the back.
The Secret Passage
You will head your way through the first passage and enter a room. When you get there the Gray Lady is gracious enough to open a second one for you. Head down that passage, and when Egon gives you the go ahead, rip off the boards. After you blast your way through several more golems, you will be given some new equipment. It's a kind of anti-slime slime gun. Use it to a neutralize any of the toxic black slime you encounter, and move forward. Once you wait through the cut scenes, it will be time to defeat The Gray Lady herself. This battle will be surprisingly easy. That is when your attention will be drawn to a glowing orb portal, which is going to take you to a parallel dimension New York Library.