Head back into the community center. Using the projector, turn it on and put the slide with the small circle on. Point it at the map, and make a mental note. Then point the projector at the other screen you pulled down earlier, and switch the slide to the dots. Make a mental note here, as this pattern is going to be part of a puzzle coming up.
Head out of the community center, then follow the tracks right. Keep going until you reach an X of tracks, and head left. Go all the way up to the rocks we destroyed earlier, and go through that portal. Head around the trash to the platform with the excavator bucket. Get on board, and hit the button to descend to a new area.
Head down the path, but keep on eye to your right for a metal box with vents and handles.
Once you find this box, open it up. Inside, you'll find a diagram. Flip the handle up. Then, head around and walk inside the building. You will see an alien looking blue panel next to an old cash register.
Hint: this can be used to solve a door code. Move all the way into the garage, and push the green button to open the door, connecting this area with the first area. You'll now see you are actually at the fuel depot.
Head out of the garage through the fuel depot, and head towards the water gate in the stone wall (the dam). Take the walkway up, and then head through the purple portal in the building.
Head all the way down the rock path to the green building.
Door code spoiler below:
Enter 406 as the door code.
The Villein Panel System
The device with the blue panel translates between decimal numbers entered on the calculator keyboard and their representation in the Villein system. You can enter a number on the keyboard to see the Villein representation, or connect dots on the Villein system and press the button above to see the numeric value. The Villein system is base-4 and drawn on a rotated grid of dots. The center dot is the 1's place. The 4's place is straight above the 1's place, the 16's place is to the right, the 64's place is below, and the 256's place is to the left. The value in each place is represented by the number of lines connecting the place dot to an adjacent dot.
The pattern shown on the projector back at Farley's Community Center (it looks like a 15 slanted downwards to the right) has one connection from the 256 place, two connections from the 64 place, one connection from the 16 place, one from the 4 place, and two from the 1 place. It therefore encodes 256+(2*64)+16+4+(2*1) = 406.
Since there are four dots adjacent to any given place dot, there are four different ways to represent a "1", six different ways to represent a "2", four different ways to represent a "3", and you could even enter a "4". However, the calculator will automatically correct these to a standard notation (e.g., "2" is always the two lines on the right), which would allow you to tell how to orient a diagram found in the wild, and also explains why a system with 5 possible digits is only base 4 instead of base 5. Farley's slide does not abide by this convention; the truly paranoid will wonder if someone has loaded the projector upside down or backwards.