The problem I have, being in Australia, is that these items never come up with the frequency that they do elsewhere in the world. In the past 3 months, I've seen 2 //e systems come up for sale, that's it. They just don't come up very often. And forget about spare parts!

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Even if you don't have the serial card you still will probably want a copy of ADTpro. It won't work great through the cassette port but it will work, and it provides an avenue for recreating from emulator images software disks you have that may be damaged.

As to the symptoms you're describing, well, I remember back from school Apple II's running various "booter"-style software (Particularly Broderbund's products) sometimes just wandering off into the weeds like you describe. It probably is either a bad disk or a dirty or misaligned disk drive. (Or some combination of the above.) If you get ADTpro working you could re-image the programs in question from an emulator image and try with that. Other than that there's not much hope of fixing or meaningfully diagnosing it without having other components and disks to swap in and out.