Hello

I did not have a problem with my 707 and 727 until now (knock on wood).

The audio signal path is not very long. it should be easy to trace it
with an oscilloscope or at least with an audio probe (a multimeter
probe, fed over a 470nF capacitor into an amplifier. Don't forget to
connect the ground of the amp-In with the 727's ground at the output
socket of the 727).
Program a pattern with all instruments playing on all steps.
Start that pattern
Measurement points are on the mainboard:
IC37 pin 4 (uPC624C) = DA-OUT (should be noise)
IC41 pin 3 (4051) = DEMUX IN (should be noise)
IC41 pins 1,2,4,5,12,13,14,15, = DEMUX OUT (should be the individual
instruments, but still kind of distorted)
On the Volume board all faders up:
both ends of the faders

For further investigation you need a scope:

If you do not have a signal on the D/A Out, then check
The address lines of the 4051
The Ref-input of the DA (pin 14)
The output of the Ref-MUX IC40 pin 3
The inputs of the Ref-MUX pins 1,2,4,5,12,13,14,15 (should read the
envelope voltages)
The lines of the Databus at IC36
The lines of the Databus at IC37

Especially the 4051 are known to die after some 20 or 30 years on spikes
in the supply power.

Florian