My brother had a machine shop that had old equipment, CNC etc. and he called on me every time he had problems with his machines. As was said, I picked the low hanging fruit and looked for obvious items such as bulging caps, obvious hot spots and bad traces, and, even though he had complete schematics for these, it is extremely difficult and time consuming to troubleshoot to the extent that you could look at a signal on a scope and infer any problems or issues.
The analog portions were doable with a scope, providing you had docs or clear views of traces so as to reverse engineer a circuit, but even that was sketchy and time consuming. What I did find out was that this brand of machines were still being used, even though they were obsolete to the manufacturer, but some companies had started in the sole purpose of repairing the boards for these machines. This company had rebuilt and tested boards that you could swap out with them, but it was not very cheap, but what is cheap? Your time spent for all those many hours analyzing and troubleshooting is worth something. An indexing control board, for instance, rebuilt, was $600 and well worth it if you needed it. Ten hours of downtime on this machine was worth -$1200, due to loss of production.