Well, as I wrote earlier, converting this to use an Access BE would be a huge amount of work - far more than just making local copies of linked tables. I can't justify putting that much effort into something on only a vague chance that somebody might be able to spot something.
I was thinking that it might be some library references, but moving everything to a new database does not fix the problem, even when the library references are not updated. The import action does not copy those, so code dependent on those references will not run. When I made the new copy, I hacked out everything that needed external libraries until the code would compile, and the quitting on start-up problem appeared in the new copy. So it's something that gets copied across in the standard import of forms, tables, queries, etc.
This morning, it was crapping out in the splash screen, so I removed that. It's only a cosmetic item. Started it up, and got about ten clean starts out of it, which was making me hopeful, but then it started quitting again, and once again, it is quitting AFTER all VBA code has stopped executing, and the main form is idle, waiting for user action.