Find out module versions through database dump
Import the dump file into mysql database. Create a new database in your localhost and import the db using your backup file
Browse System table.
Run below query

SELECT info 
FROM  system 
WHERE  filename LIKE  '%ctools.module%'
ORDER BY  system.name ASC 
LIMIT 0 , 30
You will see version information in info column. Search for "Version". Above information is serialized.
For Example, As you see below "Ctools" module is 6.x-1.11 version. You can do same for panels module by changing query.