Gentlemen, don your deerstalkers - the game is afoot!

[rutabaga bob]

Voltage on empty socket pin 5 reads .032

[anotherjim]

So, the 386 is faulty. Output of that should auto-bias internally to about 4.5v and you just proved it isn't shorted to 9v.

[rutabaga bob]

Okay.  So: replaced the 386, pin 5 ~4.9 volts.  That part is okay.  Did tweak knobs and get some sounds out of it.  Not like it was right after I bent pin 12 out to unground it, but got a little sonic weirdness.  Still have this problem, though: the pitch control isn't right.  It's wired right, but it causes the effect to act like a tone generator until you turn it far enough clockwise to go ultrasonic...which is near the 1:00 position.  This kills a good range of the effect.  It didn't act that way originally. 

[anotherjim]

It's possible some electro caps are damaged -  particularly the one on 4046 pin 9. If that is leaky the voltage on pin9 may not go high enough to go ultrasonic.
Then again, we should wonder how the 386 got fried. The most obvious is either overvoltage or reversed polarity. The 4046 may survive more than 9v as it can handle 20v, but I'm not sure of the grade of your chip there's LM386N-1 to LM386N-4 out there. Max is 15v except the -4 can handle 22v. The -4 is the most common but you never know 'till you look. The electro caps would probably survive over volts if for a short period.
With reverse polarity, the 4046 may survive as it's full of MOSFET body diodes that will act like reverse blocking protection diodes up to a point, but it's still possible for some damage that's changed its characteristics.

Do you know how it was powered? Even with a battery, it can damage the circuit if the battery clip momentarily makes reverse contact.

And, of course, like a lot of simple circuit bender projects, the design has no reverse polarity protection.

[rutabaga bob]

The only electrolytic is the power filter cap.  386s are -4s.  Will swap out the 4046 today when I find the other one that I've got. 

[anotherjim]

Actually, I think it's important to measure pin14 of the 4046 again. That diode from the 386 should not conduct when you aren't playing so pin14 should not be more than 0.5v less positive than the 386 pin 5. The replacement 386 may be biasing to a higher voltage than the old one.

[rutabaga bob]

386 pin 5: 4.911 V
4046 pin 14: 4.639 V

[anotherjim]

386 pin 5: 4.911 V
4046 pin 14: 4.639 V

That's ok. The diode won't be turned on. Only about 0.3v across it.
I forgot to ask what pin 2 voltage is now. At 9v the VCO should be ultrasonic. 0v it should be stopped. Pin 9 should be the same as pin2 when not playing.

[rutabaga bob]

With Depth control fully counter-clockwise:

Pin 2: 3.693 volts
Pin 9: 3.72 volts

Found my other 4046 chip.  Replacement will happen in the near future.

[rutabaga bob]

UPDATE: replaced the 4046 chip and played through the unit.  Sound is back to where it was before the 386 went bad...so the one chip trashed the other, as well.  Pitch control gives no oscillation/tone output, so that's wonderful!  Checked voltage at 386 output pin 5 and it's 4.9 volts.  Soldered a 1N4001 in place for some polarity protection, just in case.  Will give it back to my friend and let him try it again.  Hmm - poetic!  Hope this ends the saga. Thanks for the great help, Jim!

Am going to go back and listen to the demo once more; I get the impression my build has a lot more Velcro-sounding grit than the original...less usable range.  Hope, if that's true, it doesn't portend another disaster.

[anotherjim]

Good news.
That 4046 chip is one for which the term "YMMV" was meant for. It is a standard CMOS 4000 series type, but originally there were different manufacturers with their own ways of making them. This normally doesn't matter with logic except in the finer points of supply voltage and speed. There never was much point in choosing one brand over another with something like the 4011 quad nand gate except maybe the price.
The 4046 isn't pure logic, there is an analog element to the VCO so the control voltage sensitivity and the minimum and maximum frequency limits do vary between brands and production runs. As semiconductor brands got fewer some of the different chip designs have disappeared and some were taken over by bigger companies and re-branded. The TI one used to be a Harris semiconductor part. Some are only available now as SMD.

So, the short of it is that different builds of this project might not all work the same.