Re: Don't bother
Re. "But it's relatively expensive to fly him from India when the secretary's screen won't come on or you need to plugin that new NAS into the network."
If the organisation's large enough to have its own helpdesk (in which case where it's located is irrelevant to the discussion), then conducting running repairs on the user's desk makes no sense.
Hardware problems should be dealt with in the workshop. A man-with-a-van can take care of swapping out on site.
Keeping users working is a high priority.