Not sure if this is any help but if after everything you are not able to resolve the issue, I would
suggest getting some sharp diagonal cutters (the best I have ever found are Excelta #9242E but they are very expensive ($100) but they are so sharp you can easily cut the pins off an IC
right at the point where they come out of the package and gently bend them back about 1mm and then lift the plastic package out. Then simply touch the pins with a soldering iron
and lift them out. After removing all the pins put a drop of liquid flux on each pad and wick
the solder out with some fine pitch solder wick. Once you have all the pads wicked out and
can see through the holes, install IC sockets. This will make it easy to replace ICs. The Nixie
tubes are already socketed so unplug them and replace the Nixie tubes with ordinary leds
with 17k resistors in series, making sure to observe polarity. (cathodes should be toward the
lines from the ICs and ANODEs toward the +170V supply. You’ll have to figure out how to connect the leds. I would mount them on a separate perf board and find some pins that will
fit in the Nixie tube sockets. Once you have verified that the leds are connected polarity corrrect and each one connects to one of the IC outputs, you can power it up without the NIXIE tubes and the leds should light up simulating the tube filaments. This test setup
makes it possible to troubleshoot the ICs without the tubes.
“Edit: I measured the input voltages of the pins(DCBA) to be 3.4 volts.
Outputs 8 and 9 = 2.9V
Outputs 2 = 2.1V
Outputs 3 and 7 = 9V
output 0 and 6 = 2V
Output 1 and 5 = 9V
Output 4 alternates between 8.5 and 0V”
I looked at the 74141 data sheet and couldn’t tell what the output ON voltage should be but
if it is SINKING the filament current it should be close to zero (I*R(internal) = 7mA 8 some low
resistance so it should be close to zero when the output is ON. In fact, since the Nixie tube
filaments don’t draw very much current you may have to reduce the 17k resistors just to get
them to turn on. Once you have that dialed in you can test it with new ICs powering the leds
and you should be able to determine that the new ICs are working correctly. As I said at the
start, this whole approach is a last resort if nothing else works.