As @Audioguru said, the input pins 9 and 10, and the output pin 3 should always be very very close to zero.
When there is no signal present and you are measuring with a meter (not an oscilloscope).
Of course, with an oscilloscope, with no signal present they should also measure essentially zero.
And WITH a signal, you should see some AC audio signal floating around zero.
If they are more than a few milliVolts away from zero, then there is some significant problem.
I question whether your measurements (or your table of measurement numbers) is accurate?
The voltages in the "Good/No Signal" indicate a serious problem and they are what I would expect in the "No Good" columns.
There is no connection to pins 2, 6, and 11. So the voltages on those pins shouldn't matter.
The supply voltages on pins 1, 4, 5 and 7 look good.
(Although the slightly lower voltage on "Good/NoSignal pin 1" may be an indication of trouble.
It should be exactly the same as pin 5 (as in all your other measurements.)
The reference circuit form TI shows that the mute pin (pin 8 ) should be either open circuit (=mute)
or it should be connected to V- through RM (= un-mute)
I don't see anything in the TI data sheet that suggests anything like that zener diode D1.
Why did you put that zener diode there? That just seems bizarre and problematic.
But the main issue is where pins 9, 10 and 3 are up around 24 volts.
That is an indication of a catastrophic problem.
With no signal they should always be very close to zero.
And even with signal, they should average out to zero.
A voltage close to the positive or negative power rail is a huge red flag.
In particular, it is not at all clear how pin 10 could EVER get to 24V.
It should be completely DC-blocked by C1.
The only two possibilities that I can think of are:
1) There is a wiring error which shorts pin 10 to the +25 V power bus.
2) The chip has been severely damaged ("blown" or "toasted")
The "top" of R2 is connected (through R1) to the +Input (pin 10)
Can you confirm that the "bottom" of R2 is truly connected to ground 0 volts?
The voltage (relative to ground in all cases) at BOTH ends of R2 should be 0.000 V
It is easy to understand how pin 9 could get to +24V if there was +24V coming out of pin 3
With the LM3886 completely removed from the circuit the voltages on pin 3 and pin 9 should be zero.
And pin 10 should absolutely be 0.000 V
If pin 10 (with the LM3886 removed) is at zero, then that suggests that the LM3886 is blown up.
If pin 10 (with the LM3886 removed) is at some non-zero voltage, that indicates you have a wiring error.