Some old computers remain necessary because they control a machine, measuring instrument or unique software package. In those cases, “buy a new PC” is not a real solution.
Continued use also requires realism: parts age, security may be absent and old storage media become fragile. Continuity therefore means documenting the system, keeping spares and, where possible, isolating it from unnecessary network access.
When the function is clear, the risks are manageable and no reasonable alternative exists. An offline machine controller has a different risk profile from an old PC that uses the open internet every day.
Think about specific power supplies, storage media, cables, interface cards, dongles and installation files. Where possible, make images of old drives and document BIOS and software settings.
Sometimes for software, but not always for timing-sensitive hardware, dongles or old PCI or ISA interfaces. Test the complete chain before retiring the original system.
This can involve Digital, Basic repair and Electronics, depending on where the dependency lies.