I'm astounded that anyone would be able to remember such a complicated program after several decades. About all I remember from those days is:
10 PRINT "HELLO";
20 GOTO 10;
Anyone who has done any overclocking knows about that. When signals or timing are marginal, intermittentness appears. In the PC world, programs like Memtest86+ and Linpack are great at stress-testing to find marginality, but I'm not sure if such software was as common in the 8-bit era.
However, your problem kind of sounds like a power supply problem. So using a logic analyzer will maybe just produce a different result every time. So maybe check the 12V and 5V rails on an oscilloscope while turning on the computer. (Or maybe it's a problem with the reset circuit, etc.)
Thanks.
Silicon does degrade (and fails). But in my experience, most issues fall in 2 categories:
1) "Mechanical" problems. Connector problems, loose solder joints, corrosion, cracks in pcb traces, etc.
2) Power supply issues. Electrolytic capacitors are suspect #1 there (and they may not respond well to being powered after a looong time in storage).
Rules I apply:
a) If unsure how a machine looks inside (condition, mods etc): inspect internals before powering up.
b) Check that a machine is working before modifying it in any way. If not working: minimize steps to get to a working state.
c) Do mods in small incremental steps.
That way you can always backtrack to last working state.
The power supply should also be checked, and in this case, it's safety capacitors which are the risk there, since some of the older ones (RIFAs for example) tend to be hygroscopic, and if they crack they end up blowing next time mains is applied across them. I've not had any problems with power supplies killing the machine with an over voltage, but i've heard this is also a risk.
Anyhow, 45 years or so is time for a recap, and it'll do another 30 years before it's time again...