Get an original copy of the previous Access DB that has not been attempted to be open with a newer version.
Open a blank Access copy of the newer version
From the newer version, go to Import Objects. Go through all the tabs and import all objects including macros.
Once it is imported, go back to the DB Options and match the old DB version's Options.
Even if this is the same version of Access, this will improve the DB.
The Repair and Compact does little of either. Using the steps described above, I have salvaged broken databases.
It also compresses differently when the import objects are used.
It has also repaired corrupted controls on several occasions.
Just a note on Office 2013. Make sure the Service Packs are installed. There are pages of known issues for the original version.