Confused about Time Machine on 10.8

I purchased a new iMac running Snow Leopard. I have been attempting to back it up via Time Machine to an external hard drive (Western Digital My Book Essential) for several days now. I'm not a technical person, so please bear with me as I try to describe my issue.

I have 104GB of stuff on my computer. The WD hard drive holds 999GB. I reinitialized the external drive before beginning, and I verified it through Disk Utility. I have repaired permissions using Disk Utility and Onyx. The only thing I've excluded from the backup is the backup drive itself.

I have tried three times to back up with TM. Each time, TM tells me it will need between 27 hours and 3,000 days to do the job. I let it work overnight, and, when I check on it the next day, the progress bar tells me that the task will be completed in 5 seconds.

It will sit on "5 seconds" for hours, although the number of files changes:

If I restart the computer and try to begin a manual backup, TM tells me that there has never been a backup, but, clearly, something is being recorded onto the hard drive, because space is getting used up.

What am I doing wrong?

I've been looking through threads for this issue, and I can't find it, although I have seen experts requesting for a sample from the log. Here is part of the log on the latest backup that I cancelled. I don't understand log language, so please forgive me if I included irrelevant stuff:

1/6/13 11:03:55.214 PM com.apple.backupd[766]: Starting manual backup

1/6/13 11:03:56.292 PM com.apple.backupd[766]: Backing up to: /Volumes/MyBook/Backups.backupdb

1/6/13 11:03:57.331 PM com.apple.backupd[766]: Forcing deep traversal on source: "Big Sister" (mount: '/' fsUUID: B5CB7EC3-145D-3164-A7E3-2BD90A6DEB1C eventDBUUID: 71D4E79C-74C5-49D3-9AE2-C7E5FE3EF38C)

1/6/13 11:03:57.423 PM com.apple.backupd[766]: Warning: Bytes to copy estimate was negative (-1783297686)

1/6/13 11:03:57.424 PM com.apple.backupd[766]: Found 573831 files (104.9 MB) needing backup

1/6/13 11:03:57.443 PM com.apple.backupd[766]: 104.9 MB required (including padding), 870.26 GB available

1/6/13 11:06:44.437 PM System Preferences[728]: Could not connect the action backUpOnBatteryPowerPressed: to target of class TMOptionsSheetController

1/6/13 11:08:28.550 PM com.apple.backupd[766]: Copied 209 files (299.8 MB) from volume Big Sister.

1/6/13 11:08:28.563 PM com.apple.backupd[766]: Backup canceled.

Thank you to anyone who can help me do this correctly. I've been using TM for years on two other computers and have never had this perplexing problem.