It's hard to figure this out just from reading, without a file. This doesn't help, but it's probably something very simple, like pointing to the wrong relationship.
Something about this doesn't sound right:
in the copy of the 'Shared values' table created by the relationship request.
What happens if you just take the exact file that works on the Mac (put it on a thumb drive), stick the thumb drive into the PC and open it up on the PC?
I'm assuming same exact version of FileMaker on both computers.
Also are you using the same account, with the same privileges?
What you describe should work and identically in both systems.
When debugging relationship based conditional value lists, it's often helpful to temporarily put a portal to the value list's table occurrence on your layout. If the relationship is working, your portal should be able to list the same values as your conditional value list and that can tell you to take another look at your value list setup. If it does not list the expected rows, then you know that something is wrong either with the relationship or the match field values of either the layout's current record or the related records in the other table.