Did you try to recreate the field groups for the existing data? If this is the case then the problem is that the field keys are all incorrect and this would lead to what you describe (data in the database that does not appear in the fields)
When migrating from one database to another I generally just export all of the tables in the database and then import all of those tables and data into a fresh database. This preserves everything.
There is no easy way to fix this, it would be quite laborious. You would need to find each occurrence of each of the old field key values and replace them with the new field keys.
