Hello Elder,
Thanks for your help. Here are the answers to your questions :
Will you supply a few links to where the problem has been reported by several users so we can compare them?
http://www.tomshardware.co.uk/forum/280373-32-very-slow-boot-times-adding-hard-disc-system-boot
What is the "Microsoft program checking the partition integrity" that you determined that runs at startup that takes all the time?
=> This is a startup routine that checks partition integrity. Not sure what the exact process name is. I did the troubleshooting almost 9 months ago...
How much time does it take when it is misbehaving?
=> 4 minutes
How much time does it take when it is not misbehaving?
=> 30 seconds
What is the drive letter of the device where Windows is installed?
=> C
What is the drive letter of the device where your backup is installed?
=> F
Are either of these devices solid state drives?
=> System is SSD, then there are 2 others non SSD HD drives
The point is that if I disconnect the HD drive with the backup (with system image) or if I modify backup options to not include system image, then the issue goes away...