I have an Access database created more than 10 yrs back.
I have very important data in it & I think it can be opened in Access 2007 or earlier version. Currentl
Instal Microsoft 2007 Access Runtime.
from https://www.microsoft.com/en-US/download/details.aspx?id=4438
Google Drive has an extension to open MDB files.
I'm not sure how well BLOBs work because I couldn't get my images to display but all the text came up.
Best solution would be to convert existing databases BEFORE upgrading to newer version/s of Access. Surely Microsoft should be warning users about this problem when upgrades are about to be installed.
In case you just need to dump the data you can use this clever script http://youaccess.sourceforge.net . In case you are under linux / wine you can try my procedure
Non-Programming Answer: Download and install an older version of the Access Database Engine (2010 or 2007 for example, rather than 2013). Open Excel, navigate to the "Data" tab on the Ribbon and click "From Access". Import the data into Excel, and then Export to an accdb file or do whatever with it. NOTE! opening Access 2013 will trigger a re-install of the 2013 engine, so keep the 2007/2010 installation .exe around.
Programming Answer: Having installed an older version of Access Database Engine, you can use an OLEDB connection in multiple programming environments (C#, VBA, VBScript, etc.) to read/write and move Access data. Gord Thompson's answer also presents the option of jumping to SQL server and back.
See This post for a similar problem using an OLEDB connection
Connectionstrings.com is a great resource
See this post for how to setup an OLEDB connection using C#
NO, it does NOT work in Access 2013, only 2007/2010. There is no way to really convert an MDB to ACCDB in Access 2013.