Things look pretty bleak. If you ask around, everyone is all doom and gloom, but of course, they don't have the PC glow. Where others have failed, our intrepid characters will find a way out.
If you look around, there are four treasure chests here, each containing a Knot of Rust. Once you have all four, and after you've talked to anyone you wish, proceed to the Save Crystal and into the next room. You'll watch another cut scene, and be faced with a bare-knuckles brawl.
This fight shouldn't be too difficult, because even without your equipment, you can steal a potion from each of these three, and you can still use magic. The three bullies will go down with ease.
After another cut scene, you'll recover all your items from the Confiscatory. Whatever you do, DO NOT OPEN ANY OF THESE CHESTS or you will miss out on the Zodiac Spear later!
Balthier will warn you to tread lightly, but where's the fun in that? Explore freely and open any of the other chests in the area for a chance at the gambit Ally: HP < 60% and Chromed Leathers. In the center, near the north wall, is the door Fran was talking about. Proceed through the door for more story, and a new "friend".
After crash-landing, you'll find yourself in a hallway leading to a small room. There will be an alcove to your right with three chests containing Gil- might as well take it. Examine the Time-Worn Device in the main room, and Balthier will explain that it's a power relay, though it is currently not working. Head downstairs, and curiously, there's a merchant down here. Speak with him, and he'll give you a Tube Fuse (as well as try to sell you some other items). Go upstairs and install it, and, LET THERE BE LIGHT!
Head back downstairs and hit the Gate Switch next to Burrogh, and he'll explain that you need to keep an eye on the charge level- if it gets dark, all sorts of nasties come out. You start out at 70%, but there are Battery Mimics here that will suck up all the energy if you don't kill them first. Therefore, your primary objective should be to kill them fast enough that they actually restore energy rather than draining it.
If anyone in your party has Libra, you'll see that the Mimics are weak against ice. If you have Blizzard, use your gambits to be sure to take advantage of that. Take out the two Battery Mimics in this room first, before going after the Zombie and Tiny Mimics.
This next room will also have two Battery Mimics, but they'll be spread apart. Take out the first, then hold down R2 to flee from battle with the Steeling and Tiny Mimic and go murder the other Battery Mimic. As you proceed south, you'll encounter a third, and the little bastard will run right past you and down another hall to feed on energy. Chase it down and kill it too, then go back to your original route. You'll see a fork that goes to your right/behind you, and down that hall you'll find an urn with the Barheim Passage Map and another chest. There is a room off to the west that contains nothing but Mimics. You're under no obligation to go in there, but for the sake of completionism and also to murder these awful overgrown insects, I did. Your real destination lies to the south.
From this next room, there is a room off to the west. The gate switch is in there, and you have to battle your way through Flans and Bombs to get there. Don't forget that the Flans are weak to Fire- which at this point, Vaan should know too, making this a whole lot easier.
Hit the switch, which will require a 30% charge, and keep moving south. You'll start seeing Mimics who live up to their name- faking you out by disguising themselves as chests, but some of the chests in this area are real and worth opening for possible new equipment or gambits.
Head up the northeast slope, save your game, and prepare to meet the Mimic Queen.
Boss: Mimic Queen
Okay, gross. Now you know where all these Mimics are coming from, and it's not pretty. Don't worry about the Battery Mimics that she spits out. Like the little ones, mommy is also weak to ice, so set up your gambits accordingly. It's a good idea to have one party member heal if anyone drops below 60%, and another to cast Blizzard if you have it.
Even without Blizzard, you should be able to defeat the queen long before the power goes out, but if it drops too low, smash some of the Battery Mimics to bring it back up. You don't want to deal with the boss, her minions, AND the undead.
Once the queen is dead, the little ones will scatter, and the party makes for the exit in a tunnel-collapsing cutscene. It'll put you out in the Dalmasca Estersand.