The 74ls259 (as used by the Beeb for IC32) gives eight one-bit latches that are addressed individually. Here's a pinout:
The Beeb holds /CLEAR high (inactive), so only the /GATE on pin 14 is relevant. When /GATE is pulled low, the logic value at D (pin 13) is transferred and latched into one of the Q outputs Q0 to Q7 (as selected by the three select bits S0 to S2).
Before pressing break
The fact that pin 14 is pulsing is good, as that means IC31 is working*. So for your first set of measurements, it seems that the system is stuck in the following state:
- S0-S2 (pins 1-3) all low, selecting output Q0 (pin 4). Input D (pin 13) is high, and so is pin 4
So IC32 seems to be doing just what it is being asked to do by the VIA. Q0 is used to control the (active-low) /WRITE-ENABLE input of the 76489 sound chip, so IC32 is effectively being told repeatedly to keep the sound chip doing what it's already doing, and not write new data into it. (The other outputs, Q1-7, are holding whatever value they were latched at previously in the boot sequence.)
The question that comes to mind is why is the machine stuck telling the same thing over and over to the sound chip
As for IC18, pin 5 (/WE) matches pin 4 on IC32 just fine. Pin 14 is the input for the 4MHz clock, so the high clock rate might have something to do with your probe's unusual behaviour there. (See if pin 6 of IC6 behaves the same: that's the source of the 4MHz clock.)
After pressing break
The select lines of pin 1 and 2 are now high (pin 3 unchanged), meaning that the VIA is controlling latch Q3 (pin 7). This goes to the keyboard, and is the /KB ENABLE line. It makes sense for the system to want to be changing this value repeatedly, every time it checks for a keypress.
You said pin 8 is now high: that's surprising, as pin 8 should be ground! Did you make an error, perhaps? (Are you sure of the other pin numbers?)
Pin 4 being low is wrong: it's connected to the /WE of the sound chip (IC18). When this pin is low, the sound chip (IC18) interprets the values on the slow data bus (pins 1-3, 10-15) as being instructions for generating sound. The /WE line should be high when the VIA is communicating with the keyboard, but because it isn't, the control signals being sent to the keyboard are being tuned into sound.
IC31 is probably fine, and IC32 seems to be obeying instructions from the system (before pressing break). The measurements after pressing break need double-checking before I could say whether it's faulty or not. In the case that it's working fine, I'm having a think of what could cause the machine to boot after pressing break (as compared to a cold boot), and give incorrect instructions to IC32 along the way.
*There could be some timing issues, but they're unlikely