Your ground connection must be non-existant.
The voltages add up.
When you used the mains supply, there was no ground. 3.95 + 18.2 = near enough 22.15V, as was the case with the batteries.
If you connected it to the batteries again, you'll find the voltage between the battery 0V and the 0V in your device is around 4V.
I don't know why the positive is always 3.95V because you haven't posted a schematic of the device, so it's impossible to know.
You fix this by finding out where the ground wire is broken and reconnecting it. You need to remove the battery and power supply, before checking the continuity of the 0V connection with a multimeter.
I opened the case and measured the resistances (I have to set up ESD pad, wrist band and wire to ground to avoid static (that's why it is not easy to just open it up and measure anytime).
With all batteries disconnected.
The resistance between ground and +Vs is 12.69 kOhms
The resistance between ground and -Vs is 21.44 kOhms
The resistance between +Vs and -Vs is 8.75 kOhms.
Can the above tell you anything? What is supposed to be the resistance between ground and +Vs for example in normal circuit?
Btw.. In an opamp where there is only +Vs, -Vs, how is it connected to ground if there is no ground?
I'm still trying to trace it. I'm just careful because there would be many multimeter probing to avoid ESD as it costs $1600 new.