You're looking for Worksheet.Protect and Range.Locked.
Once the user has entered a value for product and you want to lock the country cells, you will need to do something like the following:
Activesheet.Unprotect
Range("Everything Except Country").Locked = False
Range("Country").Locked = True
Activesheet.Protect
Once you protect the sheet, the default for all cells is Locked, so you only need to define the areas where it should still be editable. If you want to continue locking additional cells as the user enters more data, you will need to unprotect the sheet, redefine the locked ranges and then re-protect the sheet.
I would suggest using the Worksheet_Change event with something like the following:
Private Sub Worksheet_Change(ByVal Target As Range)
if Target.Address = Range("Product").Address then
Activesheet.Unprotect
Range("Everything Except Country").Locked = False
Range("Country").Locked = True
Activesheet.Protect
end if
End Sub
You may also want to add an event or button where the sheet can reset to all cells being unprotected.