Long Backup (14 days) with Time Machine

Question

I have a 24 inch early 2009 iMac that I just upgraded to Mountain Lion.  Years ago I upgraded it to have 8 GB of memory.  (Having 8 GB of memory greatly reduced the amount of times I get the little spinning color wheel.)
After I upgraded, I checked to see if I needed any further updates, did the updates, and my iMac is up to date with all updates.
Now that i have installed Mountain Lion, I wanted to create a new full backup.  I have two Time Capsules and a LaCie 2 TB external drive.  When I attempt backing up to any of these three devices, it takes a really long time.  I have been backing up to a TC for over 9 hours as of this writing, and it has only backed up a bit less than 10 GB in that time.  This was overnight, when nothing was going on on the iMac.  I have tried backups to the other TC and the LaCie and aborted the backups after getting similarly slow times.
TM says it will be about 14 days before my backup is finished.  Total backup size is 371.85 GB
Also, Spotlight says there is 3 days remaining before it will be finished indexing my computer.
I have run a verify disk in Disk Utility, and it says the disk is fine.
When I look at the bar graph running on Disk Activity on the Activity Monitor, the red line (data written) is pretty much a wavy flat line very close to the bottom of the little graph window, with spikes every 10 or so seconds.  (I believe the data shown and the graph shows total Disk Activity for all disks that are mounted.)  There are times when the Data written/sec just sits there at 0 or 4 KB/sec or some other really low number, then it will spike up to a number over, say, 1, 2 and once in a while over 20 MB/sec.
I have done large backups like this in the past that took overnight or the better part of a day or two, but never this slow.  
Does anyone have any ideas what is wrong?

Answer 1

If you have more than one user account, these instructions must be carried out as an administrator.
Launch the Console application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad. Click Utilities, then Console in the icon grid.
Make sure the title of the Console window is All Messages. If it isn't, select All Messages from the SYSTEM LOG QUERIES menu on the left. If you don't see that menu, select
View ▹ Show Log List
from the menu bar.
Enter the word "Starting" (without the quotes) in the String Matching text field. You should now see log messages with the words "Starting * backup," where * represents any of the words "automatic," "manual," or "standard." Note the timestamp of the last such message. Clear the text field and scroll back in the log to that time. Select the messages timestamped from then until the end of the backup, or the end of the log if that's not clear. Copy them (command-C) to the Clipboard. Paste (command-V) into a reply to this message.
If there are runs of repeated messages, post only one example of each. Don't post many repetitions of the same message.
When posting a log extract, be selective. Don't post more than is requested.
Please do not indiscriminately dump thousands of lines from the log into this discussion.
Some personal information, such as the names of your files, may be included — anonymize before posting.