I believe I'm with you elizabeth, it can be figured out, but I confess I have no simplified or reliable method per se for doing so. For me although it does come down to experimenting with substitutions (or additions....or even subtractions of whatever gear, wiring or tweaks I can think to try, really), experience and just my best instinct are what I find I fall back on most. That's mostly trying to examine, as best I can, the actual nature of the type of audible noise or distortion I'm looking to remedy to see if that gives me the best suggestion of its possible cause and what component(s) may be involved.
For example, I already have some impression, by way of prior experience now, that there may be differences in sound between things like inferior connectors (whose constricted sound may be telling me it's time to either bypass or upgrade them), the overall whiteness or grayness of digital hash or noise or, say, sibilance issues that may be caused by a cart that is not quite properly aligned. Of course, the problem is that virtually any of these sounds may each well have more than one, possible, technical cause...or in fact many causes at the same time...and sometimes we can replace a component that fixes the problem without us ever being able to reach a reliable conclusion as to what it was about the component that was causing the problem.
But, listening to the nature of the sound of the problem is about my best bet toward identifying the source of the problem and I'm always aware that my first attempt may fail to impact the problem like I'd hoped, but that the process of elimination is still key. In the end however, I accept that eventually unearthing the real problem and finding a true solution for it is a certainty as an outcome and, in the face of the initial uncertainty, it just may demand both patience and persistence...but it all seems to go with the territory.