Are you sure that you have restored the complete backup?
Something must have gone wrong here.
Should I install the 3.2.69 over the existing one?
Also, I noticed in the database, that most of the jdownloads rows had a backup
You can try it but I'm not sure that this can help.
(The DB table was copied by the upgrade process from jD.)
Please can you send me the log file from the upgrade process via PM? This file should exist in /administrator/logs. Thanks.