Close all Access windows. If you still have Access 2013, Open it and change the settings to default open in Access 2007 Format. Close. Open a Blank Database in A2013, Import all objects. Save without compiling or compacting. Open in Access A2007 Look through your Tables and make sure the datatypes are correct. Compact and Repair. If you have any VBA then Open the VBA Editor and Debug/Compile. Save Close VBA Editor. Save and Close db. Open db and see if it works.
The issue most likely is that you have in your database some features available in A2013 that are not available in A2007 therfore it cannot understand it. Some Datatypes are different in A2013 than A2007 ie. Memo Field vs. Long Text.
On the other hand it could be you simply have a little corruption in your db. that can be fixed with Compact and Repair and then Debug and Compile. As Far as 2000 - 2003 being greyed out you will not be able to because of the features you selected to use in your db are not compatable with Access 200 - 2003. There are a lot of features in A2007 and newer that will not work in A200 - A2003.