Exit the lift and head right, watch the security guard get killed and head back to the lift, to the "Reserve Coolant Basin", follow this around until you come to a bridge on your left. Head across the bridge and along to corridor to a ladder. (Optional: before progressing, you can climb the hanging ceiling grating into a vent; at the end, you'll find a ventilation room with a dead soldier, some ammo... and some snarks.)
Head to the "Auxiliary Generator Access", pull the barrel onto the gap in the cable, blow the door and head through to the "Coolant Pump". Climb the ladder and go to the right, turn the coolant pump off (this will empty the "Coolant Chamber"), head down the corridor then the lift, move the barrels to form line. Go back up the lift and turn the coolant pump back on, this will raise the barrels into stepping stones. Go back down to the coolant chamber cross over to the "Coolant Exchange Access".
Follow the corridor and climb over the barrels, go up the stairs to the "Control Room", turn "Unit 1" and "Unit 2" on. Exit the "Control Room" and crouch-jump through the gap in the safety barrier on the right, then across the coolant. Head back to "Level 2 Access Lift", raise and cross the bridge. Wait for security guard to move then open the gate and place the battery in the "Power Cell Charging Station", hit the red button and wait for it to charge. drag the cell over to the "Power Cell Delivery Lift". Click the button under "Insert payload", then head to the "elevator access" door, head right back to the lift and go up to A Leap of Faith