Time Machine says, Unable to Complete Backup

Question

There seem to be a lot of variants of my problem on this forum, but each one is different. After several months working well, about 3 weeks ago the Time Machine on my iMac quit doing its backups to my Time Capsule. I get the message, "Unable to complete backup. An error occurred while creating the backup directory."
Repairing permissions, restarting the computer, and unplugging/replugging the Time Capsule did not help. Manually requesting a backup doesn't work either.
My computer knowledge is rather rudimentary, so if you reply, please please use step-by-step explanations, define any acronyms, etc.
Another question: is there a way to connect the Time Capsule to my computer by cable, and use it as effectively just an external drive. e.g. backing up by manual copying?
Here is the system log from a failed backup:
Jan 4 13:55:09 iMac /System/Library/CoreServices/backupd[8456]: Backup requested by user
Jan 4 13:55:09 iMac /System/Library/CoreServices/backupd[8456]: Starting standard backup
Jan 4 13:55:09 iMac /System/Library/CoreServices/backupd[8456]: Backup destination alias resolved to path: /Volumes/Time Capsule
Jan 4 13:55:10 iMac /System/Library/CoreServices/backupd[8456]: Disk image /Volumes/Time Capsule/iMac_000d936fb4dc.sparsebundle mounted at: /Volumes/Backup of iMac
Jan 4 13:55:10 iMac /System/Library/CoreServices/backupd[8456]: Backing up to: /Volumes/Backup of iMac/Backups.backupdb
Jan 4 13:55:13 iMac /System/Library/CoreServices/backupd[8456]: Failed to create progress log file at path:/Volumes/Backup of iMac/Backups.backupdb/iMac/2008-12-15-175337.inProgress/.Backup.252798913.05373 3.log.
Jan 4 13:55:13 iMac /System/Library/CoreServices/backupd[8456]: Event store UUIDs don't match for volume: HARD DRIVE
Jan 4 13:55:13 iMac /System/Library/CoreServices/backupd[8456]: Error: (-36) Creating directory 6C565DE2-06A5-419E-8CE8-4C56AEA21C5B
Jan 4 13:55:13 iMac /System/Library/CoreServices/backupd[8456]: Failed to make snapshot.
Jan 4 13:55:18 iMac /System/Library/CoreServices/backupd[8456]: Backup failed with error: 2
Jan 4 13:55:27 iMac /System/Library/CoreServices/backupd[8456]: Ejected Time Machine disk image.
Jan 4 13:55:28 iMac /System/Library/CoreServices/backupd[8456]: Ejected Time Machine network volume.
Jan 4 13:59:57 iMac sudo[8483]: alexander : TTY=ttys000 ; PWD=/Users/alexander ; USER=root ; COMMAND=/usr/bin/grep backupd /var/log/system.log

Answer 1

Ken,
This thread may be of interest if you have not already read it.
http://discussions.apple.com/thread.jspa?messageID=8354256&#8354256
Did you interrupt a backup at some stage or did you not eject the Time Capsule at the conclusion of a previous backup before shutting down your Mac?
Is there sufficient free space on Time Capsule to cater for your backups? The backup volume needs to be about 3 times the size of your Mac HD used space.
Chris