S0-S3 may be ok. Each of those S pins will be 1 for close to the same time period they are 0 so the DMM will average the reading to half of the total voltage. 2v isn't too bad and all four being the same is good.
The two Mux inputs though should be both close to supply volts with no button pressed and it seems that only one is.
Because each button only gets selected by a mux chip for 1/16th of the total scan time, the button pins of the mux chip only tell the truth 1/16th of the time. They will "float" at no particular level when unselected and no button is pressed. Your DMM won't see this as it ought to zero on a disconnected wire, but perhaps it's sensitive enough to read leakage in the mux chip or from the wiring. Pressing a button only connects the mux pin to 0v for 1/16th of the time, so it will only cause a tiny drop in the average reading.
Are the mux chips in sockets? Take them out and see what the Arduino mux inputs read then. They should both be 4.9 ish.
If they are good, turn off and use the DMM continuity test to look for shorts between adjacent mux pins and that a pin shorts to 0v when its button is pressed.
If the chips are not socketed, you'll have to disconnect the two mux wires. You can still do continuity checks of the mux chips, but be careful to keep probe polarity correct (negative on 0v) or else the CMOS chip pin protection diodes will conduct and fool you.
Ok some progress, I disconnected M2 from the Nano. (its S0-S3 pins are still tied with the first multiplexer, and it is still receiving voltage)
M2 is 1.8 volts disconnected from the board.
And interestingly enough, all the buttons tied to the first multiplexer actually work right now! So what is strange is that when M2 goes to the Nano, it affects buttons tied to the first multiplexer. Ex... 1st button sends out A and A# notes. It basically sends out the adjacent button's note assignment, sometimes the next 3. Odd right? What could be causing this?
When I tested it just now, I didnt even change the code to say I only have 1 multiplexer connected, and it still worke (first multiplexer buttons). So that lower voltage on M2 is definitely suspicious. Any ideas?
OK just did another test, I put M2 into Nano Pin 8 instead of 10 (adjusted the code for it). It all works except 1 button. The first input of the second multiplexer.
I tested the physical button, it works correctly, shorting to ground when pressed. The button also passes the continuity test going to the its multiplexer input. And there are no shorts to any adjacent pins. Now this is strange. The note I designated to it is C#4. When I press that button, it wont send out the note. When I push a different button, sometimes it sends out C#4 like 12 times. As if the previous presses were "held", then released when I pressed a different button. But I cant replicate this behavior though. Is this a bad chip?