Full backup not start
it can depend on low disk space on your server where the backup service is running.
You can configure the limits in Service Structure for Backup Service.
Verify also that you on the backup server have all software installed regarding which system extensions you have in the system.
Have you tried giving the Backup Service a jolt (=restart it)?
System resources have caused similar problems in the past - try moving the backup service to a different server. If this works, compare Task Manager performance/processes tabs. Maybe there is a resource hog (process) in your first server?