A disk icon with a red X should not affect the operation over on the left "Create a System image". When you select "Create a system image" Windows goes looking for available partitions to store an image. You are not locked into any partition which may have been setup in the regular Backup schedule settings.
"Change Settings" allows you to select another backup location for your file/folder backups (and image if you have that box ticked). Unless you explicitly assign a letter to an external HDD partition, the letter may change next time you connect the HDD. This would give you a red X.
I wouldn't expect "Change Settings" or the red X to have an impact on your specific problem.
If you have access to another external HDD with plenty of space do you still get an error?