Sadly you won't find a shock jockey in the maintenance room, however you will be allowed to replenish your salt supplies and to break into a new safe (you'll need 5 lockpicks to perform this action). The safe holds a medkit and several hundred silver eagles.
You must now start pursuing Slate who took the vigor you're looking for. Slate has left several electrical traps behind, however you will be able to neutralize them easily by shooting at the electric crystals.
You'll soon return to the square and you should expect to encounter heavy resistance here from Slate's men. Notice that a Fireman and a Motorized Patriot are among the ones you need to kill. Remember to use tears to your advantage and to avoid electrical traps.
A new door will open during the battle, leading to a small warehouse located to the left of the square. Make sure to explore the warehouse to find a Voxophone #32 on the table and Infusion #9 hidden inside a tool box.
Don't leave the warehouse just yet. Check one of the darker corners located opposite the entrance and you'll find a lockpick.
You must now make your way to a terrace from which Slate was dropping electrical traps. Continue pursuing him, finding several new traps along the way and dealing with small groups of enemies.