Hi, and welcome.
You're showing a Fritzing sketch you say you built.
Did you do it exactly the way you're showing in the sketch ?
So just what's in there and nothing else ?
I'm asking because i see some errors in there, just watching that Fritzing sketch (so the hardware).
First, in that sketch, there is no power supply to the 4051 chips.
They need power.
2nd. you have wired the buttons to pins 1, 2, 3, and 4 of one of those chips.
I have to assume that the small PCB's the chips are mounted on, have a 1 to 1 connections from chip to PCB pins.
So i took a peek and got me the NXP datasheet
That datasheet tells me pin 3 is the output of that chip.
You want to connect that to your Arduino input.
The first 4 inputs of the chip are on pins 13, 14, 15, and 12 respectively.
Pins 11, 10 and 9 are the select pins.
Those are the ones you should control by your Arduino and select the input you want to read.
I see a connection from pin 9 of the lower PCB to pin 1 of the upper PCB.
I guess you want to cascade, but you can't use these pins for this.
I can also see some connection from pin 1 to pin 5 on the lower PCB, but i guess that isn't really there, is it ?
Last, but certainly not least:
You have put a resistor at each pushbutton.
The value printed on it is 100 Ohms (brown, black, black).
That is a bit low as a pull down resistor, the most likely reason for those resistors to be there.
A 10 K (brown, black, orange) will do and will reduce current flow drastically.
You also need to check you are connecting the switches correct.
If they are by accident rotated 90 degrees (clockwise or counterclockwise), you can never see the switch switching and the resistor is permanent connected between the power rails.
This was what i can see by just looking at the hardware.
I just also had a quick look at the code.
You seem to scan by selecting different inputs (after you have checked your connections).
But that's all you seem to do:
Select inputs of the 4051, but then nothing...
If you post code, put that in code tags.
And post all of it, or else you keep us guessing about what's supposed to happen.